Probability and Statistics - Online Test
Q1.
Direction: Study the following information carefully and answer the questions that follow:
A committee of five members is to be formed out of 3 trainees, 4 professors and 6 engineers.
In how many ways this can be done if 2 trainees and 3 engineer to have to be included in a committee
Answer : Option B
Explaination / Solution:
If 2 trainees and 3 engineers include in committee
3C2*6C3 = 3*20 --> 60
Q2.
Direction: Study the following information carefully and answer the questions that follow:
A committee of five members is to be formed out of 3 trainees, 4 professors and 6 engineers.
In how many ways this can be done if at least 2 trainees to have to be included in a committee
Answer : Option D
Explaination / Solution:
If at least 2 trainees include in committee
3C2*10C3 + 3C3*10C2 = 3*120+1*45
= 405
Q3.
Direction: Study the following information carefully and answer the questions that follow:
A committee of five members is to be formed out of 3 trainees, 4 professors and 6 engineers.
In how many ways this can be done if 1 trainees and 4 engineers be included in a committee
Answer : Option A
Explaination / Solution:
If 1 trainees and 4 engineers include in committee
3C1*6C4 = 3*15 --> 45
Q4.
Direction: Study the following information carefully and answer the questions that follow:
A committee of five members is to be formed out of 3 trainees, 4 professors and 6 engineers.
In how many ways this can be done if 3 engineers and 2 professors or 2 trainees and 3 professor be included in a committee
Answer : Option C
Explaination / Solution:
If 3 engineers and 2 professors or 2 trainees and 3 professors include in committee
6C3*4C2 + 3C2*4C3 = 20*6 + 3*4 = 120 + 12 = 132
Q5.
Direction: Study the given information carefully and answer the questions that follow—
A store contains 3 red, 4 blue, 4 green and 4 whites’ bats.
If two bats are picked at random, what is the probability that both are white?
Answer : Option D
Explaination / Solution:
Probabilities if both are White
4C2/15C2 = 6/105 → 2/35
Q6. If four bats are picked at random, what is the probability that two are blue and two is green?
Answer : Option A
Explaination / Solution:
Probability if two are Blue and two are Green =
[(4C2*4C2)/15C4] = (6*6)/1365 → 12/455
Q7. If three bats are picked at random, what is the probability that at least one is green?
Answer : Option D
Explaination / Solution:
Probability if at least one is green
[1-(11C3/15C3)] = [1-(165/455)] → 58/91
Q8. If two bats are picked at random, what is the probability that either both are red or both are white?
Answer : Option B
Explaination / Solution:
Probabilities if both either are Red or either are White
(3C2 + 4C2)/15C2 = (3 + 6)/105 → 3/35
Q9. If two bats are picked at random, what is the probability that none is white?
Answer : Option B
Explaination / Solution:
Probabilities if none are white
[11C2/15C2] = (55)/(105) = 11/21
Q10. Direction: what will come in the place question mark in question given below?
10, 14, 18, 22, ?
Answer : Option D
Explaination / Solution:
Series Pattern is+4,
So next series 22+4 = 26
