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How do you find the probability of a single event?

Mario Banuelos, PhD
Associate Professor of Mathematics
Mario Banuelos is an Associate Professor of Mathematics at California State University, Fresno. With over eight years of teaching experience, Mario specializes in mathematical biology, optimization, statistical models for genome evolution, and data science. Mario holds a BA in Mathematics from California State University, Fresno, and a Ph.D. in Applied Mathematics from the University of California, Merced. Mario has taught at both the high school and collegiate levels.

Mario Banuelos, PhD

Associate Professor of Mathematics

Expert Answer

In general, you take the total number of potential outcomes as the denominator, and the number of times it may occur as the numerator. If you're trying to calculate the probability of rolling a 1 on a 6-sided die, the side with the 1 occurs once and there's a total of 6 sides, so the probability of rolling a 1 would be 1/6.

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Question

What are the rules of probability?

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This answer was written by one of our trained team of researchers who validated it for accuracy and comprehensiveness.

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Staff Answer

The 3 basic rules, or laws, of probability are as follows. 1) The law of subtraction: The probability that event A will occur is equal to 1 minus the probability that event A will not occur. 2) The law of multiplication: The probability that events A and B both occur is equal to the probability that event A occurs times the probability that event B occurs, given that event A has occurred. 3) The law of addition: The probability that event A or event B occurs is equal to the probability that event A occurs plus the probability that event B occurs minus the probability that both events A and B occur.

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How do you find probabilities with percentages?

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To calculate a probability as a percentage, solve the problem as you normally would, then convert the answer into a percent. For example, if the number of desired outcomes divided by the number of possible events is .25, multiply the answer by 100 to get 25%. If you have the odds of a particular outcome in percent form, divide the percentage by 100 and then multiply it by the number of events to get the probability.

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Question

Is there a probability calculator?

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There are numerous probability calculators online, including some that show their work so you can see what steps were involved in the calculation. Do a search for "probability calculator."

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Question

You have a pot with 100 balls. 20 of them are red, 50 are blue and 30 are green. You decide to draw 5 balls from the pot without replacement. What is the probability of drawing five blue balls?

Community Answer

First, you find the probability of drawing one blue ball: there 50 blue balls out of 100 total balls, so 50/100. If the balls are drawn without replacement, then after every draw there will be one fewer ball in the pot, so the total number of balls for the second draw is 99. Since the first ball drawn was blue, for the second draw there are only 49 blue balls in the pot, so the probability of drawing a second blue ball is 49/99. This continues for all 5 balls drawn, so the probability of drawing five blue balls can be calculated by: p=(50/100)*(49/99)*(48/98)*(47/97)*(46/96).

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Question

How can I determine probability when picking random numbers?

Community Answer

It depends on the range of the random number generator. For example, if the range is 1 through 9, the probability of getting a specific number is 1/9.

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Question

If I rolled a regular six sided die, what is the probability of getting a 5?

Community Answer

The answer would be 1/6, or approximately 17%.

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Question

I am doing an experiment and I want to find out the probability that a seed will germinate without water. How can I calculate this?

Community Answer

Since a seed will not germinate without water, the probability will be zero.

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Question

If two numbers are selected from 1 to 50, what is the probability that they will be divisible by 3 or 5?

Community Answer

There are 16 multiples of 3 in the 1 - 50 range (3, 6, 9, 12, 15, etc.). There are 10 multiples of 5 in the 1 - 50 range (5, 10, 15, 20, etc.). Of the multiples of 5, there are three which are also multiples of 3; i.e., 15, 30, 45. So the "winning" values are 16 + 10 - 3 duplicates = 23. In the first selection there are 23 "winning values" out of 50; in the second selection (assuming the original number is no longer available for the draw), there would be 22 "winning values" remaining out of the 49 numbers. The probability then is (23/50) * (22/49) = 0.2065, or 20.65%.

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Question

If a 6 sided die is tossed once, what is the probability of getting 1 or 2?

Community Answer

2/6, since the die is tossed once, the chance to get 1 is 1/6 or to get 2 is also 1/6. Therefore 1/6 + 1/6=2/6 or 1/3 or 0.333.

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Question

How do I calculate probability in football matches?

Community Answer

You can't really. The only thing you can go off of is their skill. Keep in mind that the players are human too, and they might have a bad day where they don't play as well as they usually do.

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Question

A fair coin is tossed 3 times in a row. What is the probability that heads will appear exactly two times?

Community Answer

For this problem, it is helpful to draw a tree diagram. Branching out, you will have either an H or T for the first toss. For your second toss, you will now have an H and T branching out from each H or T from before. Do this for a third toss. You will end up with 2^3 possibilities, or 8 possibilities. Now you trace the path of 3 letters to see how many ways you can find exactly 2 H's, which is 3 (HHT or HTH or THH) which equals 3/8.

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Question

When calling a coin toss, is the probability of winning each one of six tosses the same as the probability of winning all six times in a row?

Community Answer

No. The chance of winning an individual toss is 50% (1/2), assuming a fair coin and a random toss. However, winning multiple tosses in a row is a dependent event - to get a streak of correct tosses, you have to win not only the current toss, but also the previous tosses. The probability of winning all six tosses is (1/2)^6, or (1/2) (1/2)*(1/2)*(1/2)*(1/2)*(1/2), which equals 1/64, or a 1.5625% chance.

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Question

The weather channel stated that we have a 75% chance of being hit by a hurricane. What is the probability?

Community Answer

You just listed the answer, 75%.

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Question

What is the probability of drawing a face card or black card from a standard deck?

Community Answer

Since there are 4 colors and 3 face cards for each, that means 12 cards are face cards in a standard 52 card deck. The chances of pulling a face card out of a full deck of cards is 12/52. The chances of pulling a black card out of that deck is 26/52 or 1/2, since two of the four colors are black and there are 26 cards for each color.

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Question

Given a set of numbers N = {1, 3, 4, 5, 7}, what is the probability of choosing an even number?

Community Answer

Since there is 1 even number (4) out of 5 possible choices, the probability of choosing an even number is 1/5 or 0.20.

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What is the probability of rolling an 8 on two fair dice?

Community Answer

There are 36 possible combinations (1-1, 1-2, etc.). Count up the number of combinations of 8 (2-6, 3-5, 4-4, 4-4, 5-3, 6-2). Divide total number of possibilities (36) by the number of combinations of 8 (6). The probability is 1/6th.

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Question

What do the (and) and (or) mean? Example: P(female(and)smoker); P(female(or)smoker).

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"Female and smoker" refers to all persons who are both female and a smoker. "Female or smoker" refers to all persons who are female and all persons who are smokers, including all persons who are both female and a smoker, as well as all persons who are only one or the other.

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In a bag of candy, there are 4 Tootsie Rolls, 3 lollipops, 5 Hershey Kisses, and 6 Starbursts. If I select one piece of candy at random, what is the probability that it will be a lollipop?

Community Answer

There are 18 possible outcomes in this situation, 3 of which are a lollipop being chosen. 3/18 = 0.1666 = 16.66%.

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What are the chances of me winning a lottery if there are 5 winners and 995 losers?

Community Answer

0.5%, because there are 1000 possible outcomes. 1000/5 is simplified into 1/200. 1/200 is equal to 0.5%.

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I have a pot with 5 red, 6 yellow and 3 green balls. If I draw 2 random balls from the pot what is the probability that both balls will be the same color?

Community Answer

(5C2+6C2+3C2)/(5+6+3)C2. You may draw any 2 of the 5 red balls, any 2 of the 6 yellow balls and any 2 of the 3 green balls. Divide this by the total number of possibilities, i.e. drawing 2 out of the 13 balls given.

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How do I find the probability of who is to come in first, second, and third in a contest with 10 people?

Community Answer

1/10 of the people will come in first; then you have 9 people left, so 1/9 of the people will come in second. Finally, 1/8 of the people will come in third. Of course, this is all based on the presumption that they are all equal.

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Question

If a name is drawn randomly from 40 names, then I have a 1 in 40 chance. What would be the probability of my name not coming in 60 separate draws?

Community Answer

The probability of your name not being drawn is 39/40. For 60 draws, the required probability is (39/40)^60.

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A jar contains 10 red balls, 6 blue balls and 7 yellow balls. If two balls are picked at random, what is the probability that they are of the same color?

Community Answer

Ans :- (10/24+9/23) * (6/24+5/23)*7/24+(6/23). Assuming the balls are picked up without replacement.

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What is the probability of matching a computer-generated 5-digit number?

Community Answer

When guessing the match, there would be 100,000 possibilities (from 00000 to 99999), so the chance of matching a specific 5-digit number in 1 attempt would be 1/100,000, which is .001 percent.

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How can I determine the odds of a certain card getting drawn out of a deck of cards?

Community Answer

There are 52 cards in the deck, so the odds are 1 out of 52. If you draw the wrong card but continue drawing, each time you draw, your odds increase, so the second draw would be 1 out of 51.

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How do I set the following up to solve? "Find the probability that a worker is not female or saving one month's income or more."

Community Answer

Find the probability that a worker is female and saving less than one month's income. Subtract that answer from 100% and you have your answer.

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Question

What is the probability of obtaining 7 heads in a row when flipping a coin?

Community Answer

1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 1/64, or a 1 in 64 chance.

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How do I calculate the probability of beauty?

Community Answer

The golden ratio being applied to facial symmetry is probably the closest thing to a probability of beauty being found, that and waist to hip ratio for women and height for men. The other idiosyncratic preferences people have wouldn't translate to meaningful numbers as easily.

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What are the chances of one specific card being turned over?

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Because there are 52 cards in a standard deck, the chance of one specific card being pulled out is one in 52.

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