Question

As of October 31, 2008, 62% of tax refunds for the 2008 tax season were issued through direct deposit. If two refunds are selected at random the probability that both were issued be direct deposit is 0.49. What is the probability at least on the refunds is issued by direct deposit

Answer 1

The probability that at least one of the refunds is issued by direct deposit = 0.75

Explanation:

First of all, let us define the events;

Let A represent the event that the first refund was issued through direct deposit. Thus, P(A) = 0.62

Let B represent the event that the second refund was issued through direct deposit. Thus, P(B) = 0.62

We are told that; P(A ⋂ B) = 0.49

Now, from additive rule, we can define the event of either A or B occurring as;

P(A ⋃ B) = P(A) + P(B) - P(A ⋂ B)

Thus,

P(A ⋃ B) = 0.62 + 0.62 - 0.49

P(A ⋃ B) = 0.75