1 For a draw of a single card from a wellshuffled deck show

1. For a draw of a single card from a well-shuffled deck, show that the events H,J, that is, the card is a heart or jack respectively, are independent. 2. Suppose we lay out the cards from a well-shuffled 52-card deck. Show that the following events are dependent:

Solution

P(H) = 13/52 and P(J) = 4/52

P(HJ) = 1/52 = P(H) P(J)

Hence they are independent.

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P(A) = 1/52 P(B) = 1

P(AB) = 1/52C2 hence not equal not independent.

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symbols not clear

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Very long solution

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5) III one is red is given

P(iii red/first two red) = 3c2/6c2*1/4 = 1/20

P(iii red/first two blue)= 3c2/6c2*1/4 =3/20

P(iii red/first two red and blue) = 1-1/20-3/20 = 16/20

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6) 13c211C29C27C2/52C239C226C213C2

7) 7) 4/52C4

8)

8)

9) P 10th card if first ace = 48C94C1/52C10

10) P(total <=7) = P(not drawing 1 nickel and 1 penny)

= 1-1/3 = 1/3

P(nickel and dime ) = 1/3

Conditional prob = 1/3