Question

A single card is drawn from a standard​ 52-card deck. Let B be the event that the card drawn is a black​, and let F be the event that the card drawn is a face card. Find the indicated probability.P(B′∪F) = ?

Answer 1

Answer:

0.6154 or 61.54%

Step-by-step explanation:

The joint probability P(B′∪F) is given by the sum of each individual probability minus the intersection between both probabilities (red face cards).

$P(B'\cup F) = P(B')+P(F)-P(B'\cap F)$

The inverse probability of a card being black is also the probability of a card being red, which is 26 in 52. There are 12 face cards in a 52-card deck, 6 of which are not black, therefore:

$P(B'\cup F) = \frac{26}{52} +\frac{12}{52}-\frac{6}{52}\\P(B'\cup F) = \frac{32}{52} = \frac{8}{13} =0.6154$