CAT Question Bank  Probability

Q15) After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope?

Q16) Three numbers are to be selected at random without replacement from set of numbers (1,2,3,........n). The conditional probability that the third number lies between the first two, if the first number is known to be smaller than the second?

Q17) An urn contains 5 red, 1 black, few white and few blue balls.The probability of picking out 1 white ball is 1/5 and probability of picking out 1 blue ball is 1/2. When three balls are picked at random, what is the probability that none of them is blue?

Q18) Given that the product of the digits of a 4 digit number abcd with distinct nonzero digits is a multiple of 3, what is the probability that the product will also be a multiple of 9 ?

Q19) If 3 consecutive letters are selected at random from the English alphabet, then the probability that all three are consonants is:
a) 1/2
b) 11/24
c) 5/12
d) 7/12

Q20) You're about to get on a plane to Seattle. You want to know if you should bring an umbrella. You call 3 random friends of yours who live there and ask each independently if it's raining. Each of your friends has a 2/3 chance of telling you the truth and a 1/3 chance of messing with you by lying. All 3 friends tell you that 'Yes' it is raining. What is the probability that it's actually raining in Seattle?

Q21) During a fest, 100 students are arrested on suspect of bad activities. Each is given a test. From past experience it is know that the test is 90% reliable when administered to a guilty person and 98% reliable when given to some one who is innocent. Suppose that of the100 guys taken into custody, only 12 were actually involved in any wrong doing. If the probability that a given suspect in innocent given that the test says he is guilty is x/y where x and y are relatively prime, find the value of x + y

Q22) An intelligence agency decide a code of 2 digits selected from 0, 1, 2 ... 9. But the slip on which the code is handwritten, allows confusion between the top and the bottom, because these are indistinguishable. Thus, for example the code 81 should be confused with 18. How many codes are there such that there is no possibility of any confusion?
a) 25
b) 75
c) 80
d) 70
e) None of these

Q23) There are 100 passengers boarding a100 passenger airplane. When passenger 1 gets onto the plane, he is disoriented, so he randomly picks a nearby seat. Each of the remaining passengers (2, 3, 4, etc...) get onto the plane & take their seat if it is available or picks one of the remaining seats at random nearby. What is the chance that the last passenger (passenger 100) will get his seat ?

Q24) You are given a box with 20 cards in it. 10 of these cards have the letter ‘I’ printed on them. The other ten have the letter M printed on them. If you pick up 3 cards at random and keep them in the same order, the probability of making the word IIM is:

Q25) In a tennis match probability that Amit beats Sumit is 3/5 . Probability that Sumit beats Sunil is 3/5 . Probability that Sunil beats Amit is also 3/5 . If Sumit and Sunil play the first match and the winner plays against Amit what is the probability that Amit wins ?

Q26) Kurt, a painter, has 9 jars of paint:
4 are yellow
2 are red
rest are brown
Kurt will combine 3 jars of paint into a new container to make a new color,
which he will name accordingly to the following conditions:
Brun Y if the paint contains 2 jars of brown paint and no yellow
Brun X if the paint contains 3 jars of brown paint
Jaune X if the paint contains at least 2 jars of yellow
Jaune Y if the paint contains exactly 1 jar of yellow
What is the probability that the new color will be Jaune
a) 5/42
b) 37/42
c) 1/21
d) 4/9
e) 5/9

Q27) The probability that in a household LPG will last 60days or more is 0.8 and that it will last at most 90 days is 0.6. the probability that the LPG will last at most 60 to 90 days is
a) 0.40
b) 0.75
c) 0.50
d) None of these

Q28) A softball team plays two games each weekend, one on Saturday and the other on Sunday. The probability of winning the game scheduled for next Saturday is 3/5 and the probability of winning the following game, scheduled for Sunday, is 4/7. What is the probability that the team will win at least one of the two games?

Q29) A box contains 20 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is :
(a) 4/9
(b) 7/19
(c) 12/19
(d) 21/95

Q30) Two squares are chosen at random on a chessboard. What is the probability that they have a side in common?

@rowdyrathore 5/48

@rowdyrathore 1/27

@rowdyrathore  Solution pls.