Question

Calculate the following statistics:

(a) P(A ∩ B), P(A), and P(Bc) when P(B) = 0.5, P(A ∪ B) = 0.6, and P(A | B) = 0.2.
(b) Use the ALEKS calculator to find P(t ≤ -1.3) for a t-distribution with 5 degrees of freedom.

Answer 1

To find P(A ∩ B), use the formula P(A ∩ B) = P(B|A) * P(A). To find P(Bc), use the formula P(Bc) = 1 - P(B).To find P(Bc), we use the formula P(Bc) = 1 - P(B). Given that P(B) = 0.5, we can calculate P(Bc) = 1 - 0.5 = 0.5.

Step-by-step explanation:

To find P(A ∩ B), we can use the formula P(A ∩ B) = P(B|A) * P(A), since A and B are independent events.

We are given that P(A) = 0.2 and P(B) = 0.3.

Since A and B are independent, P(B|A) = P(B) = 0.3. Therefore, P(A ∩ B) = P(B|A) * P(A) = 0.3 * 0.2 = 0.06.

To find P(Bc), we use the formula P(Bc) = 1 - P(B). Given that P(B) = 0.5, we can calculate P(Bc) = 1 - 0.5 = 0.5.