All the jacks, queens, kings, and aces of a regular 52 cards deck are taken out. The 16 cards are throughly shuffled and may opponent, a person who always tells the truth, simultaneously draws two cards at random and says, "I hold at least one ace". The probability that he holds two aces is (a)2/8 (b)4/9 (c)2/3 (d)1/9

Five cards-the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards: One card is selected at random. (i) What is the probability that the card is the queen? (b) If the queen is selected and put aside (without replacement), what is the probability that the second card selected is (a) an ace? (b) a queen?

A bag contains 10 mangoes out of which 4 are rotten. Two mangoes are taken out together. If one of them is found to be good, the probability that other is also good is (a) 1/3 (b) 8/(15) (c) 5/(18) (d) 2/3

Cards are drawn one-by-one at random from a well-shuffled pack of 52 playing cards until 2 aces are obtained from the first time. The probability that 18 draws are obtained for this is

There are two urns Aa n dB . Urn A contains 5 red, 3 blue and 2 white balls, urn B contains 4 red, 3 blue, and 3 white balls. An urn is chosen at random and a ball is drawn. Probability that the ball drawn is red is a. 9//10 b. 1//2 c. 11//20 d. 9//20

A poker hand consists of 5 cards drawn at random from a well-shuffled pack of 52 cards. Then the probability that a poker hand consists of a pair and triple of equal face values (for example 2 sevens and 3 kings or 2 aces and 3 queens etc.) is-

A bag contains b blue balls and r red balls. If two balls are drawn at random, the probability of drawing two red balls is five times the probability of drawing two blue balls. Furthermore, the probability of drawing one ball of each color is six times the probability of drawing two blue balls. Then (a) b+r=9 (b) b r=18 (c) |b-r|=4 (d) b//r=2

An urn contains 3 red balls and n white balls. Mr. A draws two balls together from the urn. The probability that they have the same color is 1/2 Mr. B. Draws one balls form the urn, notes its color and replaces it. He then draws a second ball from the urn and finds that both balls have the same color is 5/8. The possible value of n is (a) 9 b. 6 c. 5 d. 1

The numbers 2,3,4,5 and 6 written on five pieces of paper. Theses pieces of paper are put in a bag and then mixed thoroughly. A man draws at random two pieces of paper from the bag one after the other without replacement. Describe the following events associated with this random experiment : A : the number on the first piece is less than the one on the second piece, B: the sum of the numbers on the two pieces is 8 or 9 , C: the number on the first piece is odd and D: the number on the second piece is greater than 4. Is there any pair of events which are mutually exclusive?

Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let X denote the random variable of number of aces obtained in the two drawn cards. Then P(X = 1) + P(X = 2) equals