Question

rita rolls a standard, 6 - sided die. let a be the event that the number she rolls is even. let b be the event that the number she rolls is less than 6. complete the paragraph. the conditional probability of b given a is the probability that the number rita rolls is. the conditional probability of b given a is.

Explanation:

Step1: Determine the sample space for event A

Event A (even number): \(A=\{2,4,6\}\), so \(n(A) = 3\).

Step2: Determine the intersection of A and B

Event B (number less than 6): \(B=\{1,2,3,4,5\}\). The intersection \(A\cap B=\{2,4\}\), so \(n(A\cap B)=2\).

Step3: Calculate the conditional probability \(P(B|A)\)

By the formula \(P(B|A)=\frac{P(A\cap B)}{P(A)}=\frac{n(A\cap B)}{n(A)}\). Substituting the values, we get \(P(B|A)=\frac{2}{3}\).

Answer:

The conditional probability of \(B\) given \(A\) is the probability that the number Rita rolls is even and less than \(6\). The conditional probability of \(B\) given \(A\) is \(\frac{2}{3}\).