Probability - Aptitude Questions and Answers Part 2

6. Rishabh studies with the help of flash cards. He has a set of 30 flash cards out of which 17 cards are white and rest are grey. 4 white and 5 grey cards are marked ENGLISH. Find the possibility of choosing a grey card or an "ENGLISH" Card randomly from the set.

a.9
13
b.13
30
c.17
30
d.22
30

Answer: c.17
30

Explanation:

Probability =What we want
Total
OR = add       AND = multiply


We want grey card OR ENGLISH card
There are 30 - 17 = 13 grey cards
There are 4 + 5 = 9 ENGLISH cards
Total cards = 30
Also 5 grey cards are ENGLISH cards.
So probability =13+9-5=17
30303030

Remember:
This subtraction is needed a grey card gets counted twice - once in 13 grey cards and once again in 9 ENGLISH cards.


7. There are 6 orange, 2 pink, 4 yellow and 3 green towels in a carton. What is the probability of picking up 2 orange towels randomly.

a.1
7
b.2
15
c.2
7
d.6
15

Answer: a.1
7

Explanation:

Probability =What we want
Total
OR = add       AND = multiply


We want 2 orange towels
That means choose one AND then choose other from remaining towels
There are 6 orange towels
Total 15 towels
So probability for 2 orange towels =6x5=1
15147

Remember:
Here we reduce the denominator i.e. total number of towels because once we remove a towel from the box we do not put it back in the box.
So while removing the 2nd towel, there are only 15 - 1 = 14 towels in the box.


8. Anupam travels with his two friends to Australia. In his bag, he has 6 black, 4 red, 2 white and 3 blue shirts. On Christmas eve all three of them chose to wear shirts from Anupam's collection. Find the probability of 2 red shirts and 1 blue shirt being chosen randomly.

a.7
2730
b.7
435
c.18
455
d.7
15

Answer: c.18
455

Explanation:

We want 2 red and 1 blue shirt
There are 4 red shirts and 3 blue shirts
Total = 15 shirts
You can choose blue shirt 1st, then red shirt and then red shirt
Probability =3x4x3=6
151413455
OR You can choose red shirt 1st, then red shirt and then blue shirt
OR You can choose red shirt 1st, then blue shirt and then red shirt
For all 3 the probability remains same =6
455
We need to add these 3 probabilities to get total probability
Total probability =6+6+6=18
455455455455


9. Out of 6 black, 4 red, 2 white and 3 blue marbles in a box, find the probability of choosing at least 1 red marble when 4 marbles are randomly picked.

a.24
455
b.69
91
c.22
91
d.4
15

Answer: b.69
91

Explanation:

Choosing 4 marbles means 1st marble AND then 2nd AND then 3rd AND then 4th marble
At least 1 red marble means there can be 1, 2, 3 or 4 red marbles.
So, Probability of choosing red = 1 - Probability of not choosing red
If we remove red marbles, then 15 - 4 red marbles = 11 marbles remain.  
We have to choose 4 out of these 11.
So Probability of choosing 4 marbles which are not red =11x10x9x8=22
1514131291
∴ Probability of picking at least 1 red marble = 1 -22=69
9191

Remember:
Here we reduce the denominator i.e. total number of marbles because once we remove a marble from the box we do not put it back in the box.
So while removing the 2nd marble, there are only 15 - 1 = 14 marbles in the box. Same is for 3rd and 4th marbles.


10. Prithvi rolled a dice twice and he saw that the addition of two numbers that appeared on the top face was 8. Find the probability of getting a 4 on the top face of the dice in first throw.

a.1
36
b.2
36
c.1
6
d.1
5

Answer: a.1
36

Explanation:

A dice has 6 faces.
So there are 6 possible outcomes
Dice is rolled once AND then again.
So total possibilities = 6 x 6 = 36

The sum should be 8 of the 2 throws.
So which combination of numbers from 1 to 6 will yield us a sum of 8?
They are - (2,6); (6,2); (3,5); (5,3); (4,4)

So there are total 5 possibilities where addition is 8.
But only 1 possibility where first throw of dice is 4.
So, Probability for first throw to be 4 and sum to be 8 =1
36

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