Probability

Question 41

Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more than 100 hours is :   Note : This question was asked as Numerical Answer Type.

• 0.55
• 0.7
• 0.4
• 0.35

Question 42

Suppose that the expectation of a random variable X is 5. Which of the following statement is True?  

• There is a simple point at which X has the value 5.
• There is a simple point at which X has value greater than 5.
• There is a simple point at which X has a value greater than or equal to 5.
• None of the above.

Question 43

When a coin is tossed, the probability of getting a Head is p,0<p<1. Let N be the random variable denoting the number of tosses till the first Head appears, including the toss where the Head appears. Assuming that successive tosses are independent, the expected value of N is

• 1/p
• 1/(1−p)
• 1/p2
• 1/(1−p2)

Question 44

A sample space has two events A and B such that probabilities P(A ∩ B) = 1/2, P(A\') = 1/3, P(B\') = 1/3. What is P(A U B)?

• 11/12
• 10/12
• 9/12
• 8/12

Question 45

What is the probability that in a randomly chosen group of r people at least three people have the same birthday?

• A
• B
• C
• D

Question 46

In how many ways can b blue balls and r red balls be distributed in n distinct boxes?

• [(n+b-1)!(n+r-1)!]/[(n-1)!b!(n-1)!r!]
• [(n+(b+r)-1)!]/[(n-1)!(n-1)!(b+r)!]
• n!/(b!r!)
• [(n+(b+r)-1)!]/[n!(b+r-1)!]

Question 47

• A
• B
• C
• D

Question 48

A random variable x takes values 0, 1, 2, ... with probability proportional to (x+1)(1/5)^x. The probability that x <= 5 is:

• 0.6997
• 0.7997
• 0.8997
• 0.9997

Question 49

Consider two events E1 and E2 such that probability of E1, Pr[E1]=1/2, probability of E2, Pr[E2]=1/3, and probability of E1 and E2, Pr[E1 and E2]=1/5, Which of the following statement is/are True?

• Pr[E1 and E2] is 2/3
• Events E1 and E2 are independent.
• Events E1 and E2 are not independent.
• Pr[E1/E2]= 4/5

Question 50

A die is rolled three times. The probability that exact one odd number turns up among the three outcomes is

• 1/6
• 3/8
• 1/8
• 1/2