A bag contains 5 red and 3 green balls. Another bag contains 4 red and 6 green balls. If one ball is drawn from each bag. Find the probability that one ball is red and one is green.
Answer: D Let A be the event that ball selected from the first bag is red and ball selected from second bag is green. Let B be the event that ball selected from the first bag is green and ball selected from second bag is red. The, P(A)= 5/8 *6/10 = 3/4 and P(B)= 3/8 * 4/10 = 3/20. Hence required probability = P(A)+P(B)= 3/4+ 3/20 = 9/10
Q. No. 14:
The odds against an event is 5:3 and the odds is favour of another independent event is 7:5. Find the probability that atleast one of the two events will occur.
Answer: C Let probability of the fist event taking place be A and probability of the second event taking place be B. Then P(A)= 3/(5+3)= 3/8 P(B)= 7/(7+5)= 7/12 The required event cab be defined as that A takes place and B does not take place (A or B takes place and A does not take place or A takes place and B takes place.) => {P(A)[1-(P(B)]}+{P(B)[1-P(A)]}+{P(A)P(B)} => {3/8 * 5/12}+{5/8 * 7/12}+{3/8 * 7/12}= (15+35+21)/96 => 71/96.
Q. No. 15:
The probability of success of three students X, Y and Z in the one examination are 1/5, 1/4 and 1/3 respectively. Find the probability of success of at least two.
Answer: D There are 13 spade and 3 more jack Probability of getting spade or a jack = (13+3)/52 = 16/52 = 4/13 So probability of getting neither spade nor a jack = 1- 4/13 = 9/13
Q. No. 17:
P and Q in a ring with 10 persons. What is the probability that X and Y will sit together?
Answer: A n(S)= number of ways of sitting 12 persons at round table = (12-1)!= 11!. Since two persons will be always together, then number of persons = 10+1 = 11. So, 11 persons will be seated in (11-1)! = 10! ways at round table and 2 particular persons will be seated in 2! ways. n(A)= The number of ways in which two persons always sit together = 10! * 2! P(A)= n(A)/n(S)= (10! *2!)/11! = 2/11.
Q. No. 18:
From a pack of 52 cards, 3 cards are drawn.What is the probability that one is ace, one is queen and one is jack?