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An experiment is picking a card from a fair deck. a.) What is the probability of...

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Basic Math

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

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4.3 Ratings (807 Votes)

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.
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