Question

6 multiple choice 1 point which of the following represents the intersection rule for two events independent events a and b? p(a and b) = p(a)p(b) p(a and b) = p(a)+p(b)-p(a or b) p(a and b) = p(a)+p(b) 7 fill in the blank 2 points find the probability of rolling a multiple of 3 on a 6 - sided die (enter as a fraction). type your answer... if we roll a die and flip a coin, whats the probability that the die is a multiple of 3 and the coin is tails (enter as a fraction)? type your answer...

Explanation:

Step1: Recall intersection rule for independent events

For two independent events A and B, the probability of both A and B occurring is the product of their individual probabilities. So $P(A\text{ and }B)=P(A)P(B)$.

Step2: Find probability of rolling a multiple of 3 on a 6 - sided die

The multiples of 3 on a 6 - sided die are 3 and 6. There are 2 favorable outcomes out of 6 total outcomes. So the probability $P=\frac{2}{6}=\frac{1}{3}$.

Step3: Find probability of die being multiple of 3 and coin being tails

The probability of getting tails on a coin flip is $\frac{1}{2}$, and the probability of getting a multiple of 3 on a die roll is $\frac{1}{3}$. Since the die - roll and coin - flip are independent events, we use the intersection rule for independent events. So the probability is $\frac{1}{3}\times\frac{1}{2}=\frac{1}{6}$.

Answer:

1. A. $P(A\text{ and }B)=P(A)P(B)$
2. $\frac{1}{3}$

$\frac{1}{6}$