# Quantitative Aptitude: Probability Questions – Set 21

1. If coins are tossed, then find the probability of getting at least 3 tails on the face.
8/9
4
1/4
1/2
2/5
Option D
Required = (5C3) + (5C4) + (5C5) = 10 + 5 + 1 = 16
total = 2^5 = 32
probability = 16/32 = 1/2

2. A bag contains 4 red balls, 2 black balls and 5 yellow balls. 3 balls are drawn randomly, find the probability of getting all balls are of red balls.
2/65
1/5
4/165
5/8
2/165
Option C
Required = 4C3 = 4
total = 11C3 = 165
probability = 4/165

3. A box contains 4 white balls and 8 blue balls. 2 balls are drawn randomly from the box in succession without replacement. What is the probability that they are different colors ?
6/17
5/12
18/25
16/33
1/8
Option D
Probability = 4/12 * 8/11 * 4/11 * 8/12 = 2 * 4/12 * 8/11 = 16/33

4. If 2 cards are selected randomly from a pack of 52 card, then what is the probability that all are face cards ?
11/221
8/25
4/225
8/29
2/441
Option A
Probability = (12C2) / (52C2)
= 12 * 11 / 52 * 51 = 11/221

5. Five men and 4 women sit in a row for eating food. What is the probability that they will sit in alternate position ?
1/26
2/85
3/82
1/126
2/ 85
Option D
Probability = 5! * 4! / 9! = 1/126

6. What is the probability that number selected from number 1, 2 , 3 … 100 is a prime number ?
2/5
1/4
5/8
1/2
4/7
Option B
Probability = 25/100 = 1/4

7. In how many different ways can the letters of the word “SHARE” be arranged ?
260
150
160
120
140
Option D
Number of ways = 5! = 120

8. One bag contains 4 blue balls and 3 green balls. Another bag contains 5 red balls and 7 blue balls. If one ball is drawn randomly from each bag then, what is the probability that both are blue balls ?
2
60
1/8
1/3
4/17
Option D
Probability = (4C1) / (7C1) * (7C1) / (12C1) = 1/3

9. A box contains 4 green balls , 2 white balls and 4 blue balls. If three balls are drawn together from the box, then what is the probability of selecting that these three balls are the same colors ?
8/17
17/18
2/25
1/15
1/30
Option D
Probability = (4C3) / (10C3) + (4C3) / (10C3)
= 1/30 + 1/30 = 1/15

10. How many words can be formed with the help of the letters of the word “SCHOOL” in such a way that all the words start with ‘L’ ?
40
60
42
85
70
Option B
Number of ways = 5!/2! = 120/2 = 60