Probability

Question 31

E1 and E2 are events in a probability space satisfying the following constraints:

 
    Pr(E1) = Pr(E2)
    Pr(EI U E2) = 1
    E1 and E2 are independent 

The value of Pr(E1), the probability of the event E1 is

• 0
• 1/4
• 1/2
• 1

Question 32

An ISP has a link of 100Mbps which is shared by its subscribers. Considering the fact that all of its subscribers are active 50% of the time and the probabilities of being active are independent, the ISP has promised 25 Mbps to its 6 subscribers. What is the probability that any subscriber gets degraded service (less than promised speed).

• 1/32
• 5/16
• 1/2
• 7/64

Question 33

Given Set A = {2, 3, 4, 5} and Set B = {11, 12, 13, 14, 15}, two numbers are randomly selected, one from each set. What is the probability that the sum of the two numbers equals 16?

• 0.20
• 0.25
• 0.30
• 0.33

Question 34

The probabilities that a student passes in Mathematics, Physics and Chemistry are m, p and c respectively. Of these subjects, the student has 75% chance of passing in at least one, a 50% chance of passing in at least two and a 40% chance of passing in exactly two. Following relations are drawn in m, p and c:

1. p + m + c = 27/20 
2. p + m + c = 13/20
3. (p) × (m) × (c) = 1/10 

• Only relation 1 is true
• Only relation 2 is true
• Relations 2 and 3 are true
• Relations 1 and 3 are true

Question 35

Suppose Xi for i = 1, 2, 3 are independent and identically distributed random variables whose probability mass functions are Pr[Xi = 0] = Pr[Xi = 1] = 1/2 for i = 1, 2, 3. Define another random variable Y = X1 X2 ⊕ X3, where ⊕ denotes XOR. Then Pr[Y = 0 ⎪ X3 = 0] = ____________.

• 0.75

• 0.50

• 0.85

• 0.25

Question 36

In how many ways can we distribute 5 distinct balls, B1,B2,...,B5 in 5 distinct cells, C1,C2,...,C5 such that Ball B,is not in cell C,Vi=1,2,...,5 and each cell contains exactly one ball?

• 44
• 96
• 120
• 3125

Question 37

A bag contains 10 blue marbles, 20 green marbles and 30 red marbles. A marble is drawn from the bag, its colour recorded and it is put back in the bag. This process is repeated 3 times. The probability that no two of the marbles drawn have the same colour is

• 1/36
• 1/6
• 1/4
• 1/3

Question 38

An unbiased coin is tossed repeatedly until the outcome of two successive tosses is the same. Assuming that the trials are independent, the expected number of tosses is

• 3
• 4
• 5
• 6

Question 39

A probability density function on the interval [a, 1] is given by 1 / x² and outside this interval the value of the function is zero. The value of a is :   Note : This question was asked as Numerical Answer Type.

• -1
• 0
• 1
• 0.5

Question 40

Consider the following experiment.

Step 1. Flip a fair coin twice.
Step 2. If the outcomes are (TAILS, HEADS) then output Y and stop.
Step 3. If the outcomes are either (HEADS, HEAD) or (HEADS, TAILS), 
        then output N and stop.
Step 4. If the outcomes are (TAILS, TAILS), then go to Step 1.

The probability that the output of the experiment is Y is (up to two decimal places). [This Question was originally a Fill-in-the-Blanks question]

• 0.33
• 0.25
• 0.5
• 0.27