3 cards are drawn successively without replacement from a pack of 52 cards. what is the probability that the first two cards are kings and third card drawn is an ace
3 cards are drawn successively without replacement from a pack of 52 cards. what is the probability that the first two cards are kings and third card drawn is an ace
the probability is a dependent probability , in which no. of sample space can be change according to question.
in a card, no. of sample space, P(S1) = 52
without replacing, the sample space in second time , P (s2) = 51
similarly in third time it will be, P(s3) = 50
Probability of a king , P ( K1) = n(K1) / n(s1) = 4/52
probability of second king = n(K2) / n(s2) = 3/51
probability of an ace in pack, n(A) / n(s3) = 4/50
therefore the probability, P(of event) = P {P(K1) and P(K2) and P(K3)}
by multiplication principle, P(E) = 4/52 × 3/51 × 4/50 = 2/5225
the probability is a dependent probability , in which no. of sample space can be change according to question.
in a card, no. of sample space, P(S1) = 52
without replacing, the sample space in second time , P (s2) = 51
similarly in third time it will be, P(s3) = 50
Probability of a king , P ( K1) = n(K1) / n(s1) = 4/52
probability of second king = n(K2) / n(s2) = 3/51
probability of an ace in pack, n(A) / n(s3) = 4/50
therefore the probability, P(of event) = P {P(K1) and P(K2) and P(K3)}
by multiplication principle, P(E) = 4/52 × 3/51 × 4/50 = 2/5225
