Consider an ordinary deck of 52 cards In this deck there are

Consider an ordinary deck of 52 cards. In this deck, there are 4 suits and 2 colors: 13 diamonds and 13 hearts (both red) and 13 clubs and 13 spades (both black). Within each suit, the 13 cards labeled as 2,3,4,5,6,7,8,9, 1O,jack,queen,king, and ace. Suppose you are drawing a single card at random from this deck. Find the following probabilities. You may enter your answer as either a fraction or a decimal. a. P(club)= 0.25 b. P(black)= 0.5 c. P(jack)= 0.077 d. P(club | jack)= 3.75 e. P(club | black)= 0.5 f. P(jack | black)= g. Based on the above calculations, we can conclude that the events draw a club and draw a black are h. Based on the above calculations, we can conclude that the events draw a jack and draw a black are D i. Based on the above calculations, we can conclude that the events draw a club and draw a jack are

Solution

d)

P(club|jack) = P(jack of clubs) / P(jack)

As P(jack of clubs) = 1/52, P(jack) = 4/52,

P(club|jack) = P(jack of clubs) / P(jack) = (1/52)/(4/52) = 0.25 [ANSWER]

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F)

P(jack|black) = P(a black jack) / P(black)

As

P(a black jack) = 2/52 and P(black) = 26/52,

P(jack|black) = (2/52)/(26/52) = 0.076923077 [ANSWER]

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g)

As P(club|jack) = P(club), then they are INDEPENDENT. [ANSWER]

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h)

As P(jack|black) = P(jack), then they are INDEPENDENT. [ANSWER]

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i)

As P(club|jack) = P(club), then they are INDEPENDENT.