Question

1.an urn containing 9 black,12 white and 15 red balls is randomly divided into 3 baskets containing 12 balls each.what is the probability that each basket will have the same number of black balls?

2.cards are drawn at random from an ordinary deck of 52,one by one without replacement.what is the probability that no king is drawn before the ace of spades is drawn?

Answer 1

SOLUTION : [1]

TOTAL BALLS IN URN = 36

NUMBER OF BLACK BALLS = 9

PROBABILITY OF BLACK BALL = 9/36 = 0.25

P=0.25

N=12

X=3

P[ X= 3 ] = BY USING BINOMIAL DISTRIBUTION , WE HAVE

P [ X=3 ] = 0.2581

[2]   Let X be the number of draws before getting the Ace of Spades and before a king is drawn

P(X = 1) = 1/52

P(X = 2) = 39/52 * 1/51 = 0.0147

P(X = 3) = 39 * 38 * 1 / ( 52 * 51 * 50)

P(X = 4) = (39 * 38 * 37 * 1) / (52 * 51 * 50 * 49)

...

P(X = x) = (39! (52-x)!) / ( (40 - x)! 52!)