# Quantitative Aptitude: Probability Questions – Set 19

1. Two dices are rolled down simultaneously, then find the probability of getting sum of results on both dices more than 8.
2/15
4/19
1/8
5/18
3/20
Option D
possible cases=(3,6), (4,5), (4,6), (5,4), (5,5)
required probability=10/36=5/18

2. A bag contains 6 blue balls and 8 pink balls. If a ball is drawn randomly from it, then find the probability of getting either pink ball or blue ball.
4
5
1
1/4
2/5
Option C
required probability=6/14+8/14=14/14=1

3. In a box there are 4 red balls and 3 blue balls. If two balls are drawn at random, then find the probability of that none is blue.
2/5
2/7
5/8
4/15
4/18
Option B
required probability=(4C2)/(7C2)
=4*3/7*6=2/7

4. A basket contains 5 white balls , 4 red balls, 2 blue balls and 3 yellow balls. If four balls are picked at randomly. What is the probability that 2 are blue and 2 are red ?
5/1002
8/968
12/1005
8/950
6/1001
Option E
required=(2C2)*(4C2)
=(2*1/2*1)*(4*3/2*1)=1*6
total=14C4=14*13*12*11/4*3*2*1
=7*13*11
probability=1*6/7*13*11=6/1001

5. When two dices are thrown simultaneously, then find the probability that sum is a prime number which is less than 8 ?
12/38
20/36
20/35
13/36
15/48
Option D
prime numbers=2,3,5,7
possibility of 2=(1,1)
possibility of 3=(1,2), (2,1)
possibility of 5=(1,4), (4,1), (3,2), (2,3)
possibility of 7=(1,6), (6,1), (2,5), (5,2), (3,4), (4,3)
required=1+2+4+6=13
total=6^2=36
probability=13/36

6. When two coins are tossed simultaneously, then find the probability of getting at least one head.
4/5
3/4
8/9
7/12
2/15
Option B
probability=3/2^2=3/4

7. If from a pack of 52 cards, 1 cards is drawn at randomly, find the probability of the card is an ace.
2/15
1/13
4/15
2/25
8/18
Option B
required=4C1=4
total=52C1
probability=4/52=1/13

8. Two cards are drawn at random from a pack of 52 cards. What is the probability that both are the queen cards ?
2/221
4/225
5/228
1/221
8/125
Option D
required=4C2=4*3/2*1=12/2=6
total=52C2=52*51/2
probability=6/26*51=1/221

9. In how many ways letters of the word ‘LAPTOP’ be arranged such that consonants always come together ?
50
75
40
72
80
Option D
required ways=3!*4!/2!=72 ways

10. A bag contains 4 red balls and 8 balls. If two balls are taken out from the bag, then find probability of at least one ball being red ?
40/85
48/65
55/64
35/66
40/86
Option D
favorable cases=(1 blue and 1 red) or ( 2 red)
probability=(4C1)*(8C1)/(12C2)+(4C2)/(12C2)
=(4*8/12*11/2*1)+(4*3/2*1/12*11)
=(4*8/11*6)+(2*3/12*11)=16/33+1/22
=32+3/66=35/66