Probability-12 (MPMET-2008)

What is the probability of getting exactly 60 marks in a paper of 100 marks?

(A)60/100      (B)1/100         (C)1/101         (D)60/101

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Probability-10 (IIT-2003)

A is targeting B, B and C targeting A. Probability of hitting the target by A,B and C are respectively 2/3,1/2 and 1/3. If A is hit then find the probability B but not C hits A.

Solution follows here:

Probability-9 (IIT-1995)

The probability of India winning a test match against West Indies is ½. Assuming independence from match to match the probability that in a 5 match series India’s second win occurs at the third test is:  

(a) 1/8          (b) 1/4        (c) 1/2              (d) 2/3

Solution follows here:

Probability-8 (IIT-2004)

Out of first 100 natural numbers, three numbers are chosen without replacement. The probability that all these numbers are divisible both by 2 and 3 is:  

(a)4/11          (b) 4/55        (c) 4/33              (d) 4/1155

Solution follows here:

Probability-7 (IIT-2003)

For a student to qualify a competitive exam, he must pass at least two out of the three exams. The probability that he will pass the first exam is p. If he fails in one of the exams, then the probability of his passing in the next exam is p/2, otherwise it remains the same. Find the probability that the student will qualify the competitive exam.  

Solution follows here:

Probability-6 (FRM)

With a portfolio that consists of 20 well-diversified A-rated bonds and assuming a default probability of 1% per annum, what is the approximate probability of sustaining no losses on the portfolio over the next 12 months?

(a)0.82          (b) 0.8        (c) 0.85              (d) 0.99

Solution follows here:

Probability-5 (FRM)

A company has a constant 7% per year probability of default. What is the probability the company will be in default after three years?

(a)19.6%          (b) 22.5%        (c) 21%              (d) 7%

Solution follows here:

Probability-4 (FRM)

There are 10 students in a class. The probability of a student getting absent is 5%. The probability of any one student getting absent is completely independent of the presence or absence of any other student. What is the probability that exactly one student gets absent?

(a)5%          (b) 50%        (c) 32%              (d) 3%

Solution follows here:

Probability-3 (FRM)

Of all the employees at an office, 40% prefer coffee and 60% prefer tea. Of those who prefer coffee, 30% are females and of those who prefer tea, 40% are female. What is the probability that a randomly selected employee prefers coffee, given that the person selected is a female?

(a)1/3          (b) 2/3        (c) 1/9              (d) 2/9

Solution follows here:

Probability-2 (IIT-JEE 2009)

A signal which can be green or red with probability 4/5 and 1/5 respectively, is received by station A, and then transmitted to station B. The probability of each station receiving the signal correctly is ¾. If the signal received at station B is green, then the probability that the original signal was green is
(a)3/5          (b) 6/7             (c)20/23                         (d)9/20
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