1 For a draw of single card from a well shuffled deck show t

1) For a draw of 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) A dish contain 1 penney, 1 nickle and 1 dime. A batch of two coins is drawn out, and you\'re told that their total valur is 7 cents or more. what is the probability that the two coins are the nickle and the dime?

3) Suppose we lay out the cards from a well shuffled 52 card deck, what is the probability that the 10th card is the first ace to be dealt?

4) Suppose we lay out the cards from a will shuffled 52 cards deck, show that the following are dependent. A: the first card is the ace of clubs. B: the first card is the ace of the hearts.

Solution

a) P(HUJ) = 13/52+4/52-1/52 = 16/52

P(J) = 4/52

P(HJ) = 1/52

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

As these are not equal H and J cannot be independent.

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1 penny 1 nickel 1 dime

2 coins are drawn.

If value >5 cents, then 2 pennies

or 1 penny, 1 nickel cannot be there.

Hence prob = 1-