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suppose that we are going to roll two fair 6- sided dice. Find the probability that both dice show a 3. (look at the information provided within the picture.) chose 1 answer choice: A.) P(both 3)= 1\2 B.) P(both 3)= 1\3 C.) P(both 3)= 1\12 D.) P(both 3)= 1\36

suppose that we are going to roll two fair 6- sided dice. Find the probability that both dice show a 3. (look at the information provided within the picture.) chose 1 answer choice: A.) P(both 3)= 1\2 B.) P(both 3)= 1\3 C.) P(both 3)= 1\12 D.) P(both 3)= 1\36

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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I had to correct this question so please answer.

Please Answer correctly and read carefully deals with the general multiplication rule in probability.

question:

suppose that we are going to roll two fair 6- sided dice. Find the probability that both dice show a 3. (look at the information provided within the picture.)

chose 1 answer choice:

A.) P(both 3)= 1\2

B.) P(both 3)= 1\3

C.) P(both 3)= 1\12

D.) P(both 3)= 1\36

Independent events: Flipping a coin twice What is the probability of flipping a fair coin and getting "heads" twice in a row? That is, what is the probability of getting heads on the fırst flip AND heads on the second flip? Imagine we had 100 people simulate this and flip a coin twice. On average, 50 people would get heads on the first flip, and then 25 of them would get heads again. So 25 out of the original 100 people – or 1/4 of them – would get heads twice in a row. The number of people we start with doesn't really matter. Theoretically, 1/2 of the original group will get heads, and 1/2 of that group will get heads again. To find a fraction of a fraction, we multiply. We can represent this concept with a tree diagram like the one shown below. 1 1 1 1/2 H %3D 4 H 1/2 1 1 1 1/2 T %3D 2 4 1 1 1 1/2 H 4 1/2 1 1 1 1/2 T 2 2 4
Transcribed Image Text:Independent events: Flipping a coin twice What is the probability of flipping a fair coin and getting "heads" twice in a row? That is, what is the probability of getting heads on the fırst flip AND heads on the second flip? Imagine we had 100 people simulate this and flip a coin twice. On average, 50 people would get heads on the first flip, and then 25 of them would get heads again. So 25 out of the original 100 people – or 1/4 of them – would get heads twice in a row. The number of people we start with doesn't really matter. Theoretically, 1/2 of the original group will get heads, and 1/2 of that group will get heads again. To find a fraction of a fraction, we multiply. We can represent this concept with a tree diagram like the one shown below. 1 1 1 1/2 H %3D 4 H 1/2 1 1 1 1/2 T %3D 2 4 1 1 1 1/2 H 4 1/2 1 1 1 1/2 T 2 2 4
We multiply the probabilities along the branches to find the overall probability of one event AND the next even occurring. For example, the probability of getting two "tails" in a row would be: 1 P(T and T) 1 2 2 4 When two events are independent, we can say that P(A and B) = P(A) · P(B) Be careful! This formula only applies to independent events.
Transcribed Image Text:We multiply the probabilities along the branches to find the overall probability of one event AND the next even occurring. For example, the probability of getting two "tails" in a row would be: 1 P(T and T) 1 2 2 4 When two events are independent, we can say that P(A and B) = P(A) · P(B) Be careful! This formula only applies to independent events.
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