Suppose that you select 2 cards without replacement from a standard deck of 52 playing cards....

Suppose that you select 2 cards without replacement from a standard deck of 52 playing cards. a) If the first card that you select is NOT a heart, what is the probability that the second card that you select IS a heart? b) If the first card that you select IS a six, what is the probability that the second card that you select IS a diamond? PLEASE SHOW ALL WORK

Solutions

Expert Solution

a) There are 13 hearts out of 52 cards.we can choose 1 heart in ways.So by the classical definition of probability ,probability of choosing 1 heart is (13/52)

Now P(2nd heart/1st not heart)= P(2nd heart,1st not heart) / P(1st not heart)

=(13/52)/(39/52)

=1/3

b)There are 4 cards numberd 6.One of them is of diamond.So there are 2 cases.i)the selected card is of diamond or ii)the selected card is not of diamond

so P(2nd card diamond/1st card is six)= P(2nd card diamond,1st card is six) / P(1st card is six)

=(P(2nd card diamond,1st card is six and diamond)+P(2nd card

diamond,1st card is six but not diamond))/P(1st card is six)

=((1/52)*(12/52)+(13/52)*(3/52)) / (4/52)

=51/208

where, P(1st card is six and diamond)=1/52 , as there are 4 six among them one is of diamond which can be choosen in 1 way and 1 card from 52 cards can be choosen 52 ways.

similarly P(1st card is six but nit diamond)=3/52, as there are 3 non diamond six.

if in first draw diamond is choosen then for 2nd draw we have 12 option so then the probability will be 12/52 otherwise that will be 13/52.

As there are 4 six so by the classical definition of probability that probability wull be 4/52.

orchestra answered 1 year ago

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