You dark two cards from a standard deck of 52 cards without replacing the first one...

You dark two cards from a standard deck of 52 cards without replacing the first one before drawing the second

a) Are the outcomes on the two cards independent? why

b)find p(ace on 1st card and kind on 2nd )

c) find p(kind on 1st card and ace on 2nd

Solutions

Expert Solution

The probability selecting of two dark cards from pack of 52 cards is

P(dark card) = (total number of dark cards/ total cards) = 26/52= 1/2

a) Are the outcomes on the two cards independent? why

No, they are dependent because the selection of second card is dependent on the first card.

b) find p(ace on 1st card and kind on 2nd )

Ans: there are two ace cards and two king cards in pack of 52 cards, while selecting first card the probability is 2/52 and for selecting second card the probability of selection of king dark card is 2/51.

p(ace on 1st card and kind on 2nd )= (2/52)*(2/51) = 0.0015

If we chose two cards from pack of 52 cards and repeated trial 10000 times than 15 times out of 10000 times we can find the ace on 1st card and kind on 2nd card.

c) find p(kind on 1st card and ace on 2nd)

Ans: there are two ace cards and two king cards in pack of 52 cards, while selecting first king dark card the probability is 2/52 and for selecting second card the probability of selection of ace dark card is 2/51.

p(kind on 1st card and ace on 2nd) =(2/52)*(2/51) = 0.0015

If we chose two cards from pack of 52 cards and repeated trial 10000 times than 15 times out of 10000 times we can find the kind on 1st card and ace on 2nd)

Thanks

orchestra answered 2 years ago

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