Question

An experiment is picking a card from a fair deck. a.) What is the probability of picking a Jack given that the card is a face card? b.) What is the probability of picking a heart given that the card is a three? c.) What is the probability of picking a red card given that the card is an ace? d.) Are the events Jack and face card independent events? Why or why not? e.) Are the events red card and ace independent events? Why or why not?

Answer 1

Total card = 52

a) P(jack | face card) = P(jack and face card) / P(face card)

                                  = (4/52) / (12/52)

                                  = 4/12

                                  = 1/3 or 0.333

b) P(heart | three) = P(heart and three) / P(three)

                             = (1/52) / (4/52)

                             = 1/4

                             = 0.25

c) P(red card | ace) = P(red card and ace) / P(ace)

                                = (2/52) / (4/52)

                                = 2/4

                                = 1/2 or 0.5

d) P(jack) = 4/52

Since P(jack | face card) is not equal to P(jack), they are not independent events.

e) P(red card) = 26/52 = 0.5

Since P(red | ace) = P(red), they are independent events.