Question

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

Explanation:

Step1: Identify sample - space of A

The event A is that the number rolled is less than 6. The sample - space of A has 5 elements: {1, 2, 3, 4, 5}.

Step2: Identify elements of A ∩ B

The event B is that the number rolled is even. The elements of A ∩ B (numbers that are less than 6 and even) are {2, 4}. So, n(A ∩ B)=2.

Step3: Calculate conditional probability

The formula for conditional probability is P(B|A)=\frac{P(A\cap B)}{P(A)}. Since P(A)=\frac{5}{6} and P(A\cap B)=\frac{2}{6}, then P(B|A)=\frac{P(A\cap B)}{P(A)}=\frac{\frac{2}{6}}{\frac{5}{6}}=\frac{2}{5}.

Answer:

\frac{2}{5}