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What is the formula for probability?

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

Probability is determined by the number of outcomes you want compared to the total number of outcomes. For example, if you roll a 6-sided die, each outcome has a 1 out of 6 probability.

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Question

How do you know when to multiply the fractions and when to add them?

Community Answer

Multiplication of probabilities is for when the event requires multiple things to happen. (For example, roll a 1 on the first die AND, having done that, roll a 4 on the second die.) The combo event has a probability of (1/6)*(1/6). Addition of probabilities is for when an event can be achieved in multiple ways that can't both happen. (For example, roll EITHER a 1 OR a 4 on a die.) The combo event has a probability of (1/6) + (1/6).

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If I tossed two fair dice. What is the probability of getting 7?

Donagan

Top Answerer

The probability is 1 in 6 (1:6 or 1/6). There are 36 possible combinations of the dice, and six of them result in a 7. For each of the six numbers that can show on die A, there is one number on die B that will result in a total of 7, so 6 of the 36 possible combinations will total 7, and 6 of 36 is 1 of 6.

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Can the probability of a single event be greater than 1?

Community Answer

No. Probabilities range from 0 to 1, with impossible events having probability 0 and certain events having probability 1. If you get a negative probability, or one greater than 1, consider rechecking your work for errors.

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Can you explain what a complementary event is?

Community Answer

Either it happens or it won't. If you have one event representing "it happens", then its complementary event represents "it won't happen". If two events are complements, then their probabilities must add up to 1.

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A bag contains 11 red buttons, 4 green buttons, 1 blue button and some yellow. The chances of choosing a yellow button is I in 3, how many yellows buttons are there?

Donagan

Top Answerer

Let x equal the number of yellow buttons. The total number of buttons is 11 + 4 + 1 + x = 16 + x. Since the chance of picking a yellow button is 1 in 3, there are 3 times as many total buttons as yellow buttons. Thus, 3x = 16 + x. Then 2x = 16, and x = 8. (To check, the total number of buttons is 11 + 4 + 1 + 8 = 24, which is 3 times 8.)

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What is the probability of getting a sum of 6 when 2 dice are thrown?

Rainy

Top Answerer

Each dice has six sides, so there are 36 possible outcomes. Five of them result in a total of six, which means that your answer is 5/36.

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Question

How do I solve probability from the beginning?

I_l1ke_gam3s

Community Answer

Probability is the number of chances out of the total amount of chances of an event.

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