The number of 3-digit numbers such that the digit 1 is never to the immediate right of 2 is
524
881
761
658
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.33
Given two independent events A and B such that P(A) =0.3, P(B) = 0.6 and P(𝐴' ∩ 𝐵') is
0.9
0.18
0.28
None of the above
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.33
The probability that a contractor gets a plumbing contract is 2 / 3 and the probability that he will not get an electric contract is 5 / 9. If the probability of getting at least one contract is 4 / 5, then the probability that he will get both the contracts is:
13/45
14/45
16/45
17/45
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.33
A can solve 90% of the problems given in a book and B can solve 70%. What is the probability that at least one of them will solve a problem, selected at random from the book?
0.16
0.69
0.97
0.20
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.33
P and Q are considering to apply for a job. The probability that P applies for the job is 1/4 , the probability that P applies for the job given that Q applies for the job is 1/2 , and the probability that Q applies for the job given that P applies for the job is 1/3 . Then the probability that P does not apply for the job given that Q does not apply for the job is
4/5
5/6
7/8
11/12
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.66
A, B and C are three mutually exclusive and exhaustive events. P(A) = 2P(B) = 6P(C). Find P(B).
0.1
0.3
0.6
0.4
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.66
Two digits out of 1, 2, 3, 4, 5 are chosen at random and multiplied together. What is the probability that the last digit in the product appears as 0?
1/5
3/5
2/5
4/5
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.66
A problem in Mathematics is given to three students A, B and C. The probability of A solving the problem is 1/2 and B not solving is 1/4. The whole probability of the problem being solved is 63/64. What is the probability of solving it by C?
6/8
7/8
5/8
4/8
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.66
In a small village, there are 87 families, of which 52 families have at most 2 children. In a rural development programme, 20 families are to be chosen for assistance, of which at least 18 families must have at most 2 children. In how many ways can the choice be made?
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.66
Roll a die.

Let A be the event that the outcome on the die is an even number.

Let B be the event that the outcome on the die is or smaller.

Let C be the event that the outcome on the die is or larger.

Choose the correct option(s)? [MSQ]

A and B are dependent events
A and B are independent events
B and C are dependent events
B and C are independent events
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00
Which of the following is/are True?

Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00

If A and B are two mutually exclusive events, then which of the following are possible: [MSQ]

Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00

[MSQ]

Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00
It is estimated that 50% of emails are spam emails. Some software has been applied to filter these spam emails before they reach your inbox. A certain brand of software claims that it can detect 99% of spam emails, and the probability for a false positive (a non-spam email detected as spam) is 5%. Now if an email is detected as spam, then what is the probability that it is in fact a non-spam email?
1/104
2/104
5/104
6/104
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.66
Find the covariance for the following data.

0.126
0.412
0.78
0.145
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.33