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Directions : Read the following questions carefully and choose the right answer.
1
The names of 5 students from section A, 6 students from section B and 7 students from section C were selected. The age of all the 18 students was different. Again, one name was selected from them and it was found that it was of section B. What was the probability that it was the youngest student of the section B? 
» Explain it
C
The total number of students = 18

When 1 name was selected from 18 names, the probability that he was of section B

=  6  =  1
18 3

But from the question, there are 6 students from the section B and the age of all 6 are different therefore, the probability of selecting one i.e. youngest student from 6 students will be 1/6

Hence, option C is correct.
2
A bag contains 35 balls of three different colors viz. red, orange and pink. The ratio of red balls to orange balls is 3 : 2, respectively and probability of choosing a pink ball is 3/7. If two balls are picked from the bag, then what is the probability that one ball is orange and one ball is pink?
» Explain it
A
Let, the number of pink balls be p

Probability of choosing a pink ball =  p
35

=>  3  =  p
7 35

=> p = 15

So, remaining number of balls = (35 – 15) = 20

Number of orange balls =  2  × 20 = 2 × 4 = 8
2 + 3

Therefore, reqd. probability =  8C1 × 15C1
35C2

=  8 × 15  =  24
35 × 34/2 119

Hence, option A is correct.
3
There are total 18 balls in a bag. Out of them 6 are red in colour, 4 are green in colour and 8 are blue in colour. If Vishal picks three balls randomly from the bag, then what will be the probability that all the three balls are not of the same colour?
» Explain it
D
Number of ways in which the person can pick three balls out of 18 balls = 18C3 = 816

Number of ways of picking 3 balls of same colour = 6C3+ 4C + 8C3 = (20 + 4 + 56) = 80

Probability of picking three balls of same color

=  80  =  5
816 51

Required probability = 1 – probability of picking three balls of same colour

= 1 –  5  =  46
51 51

Hence, option D is correct.
4
Ram and Shyam are playing chess together. Ram knows the two rows in which he has to put all the pieces in but he doesn’t know how to place them. What is the probability that he puts all the pieces in the right place?
» Explain it
B
Total boxes = 16

Total pieces = 16

Similar pieces = 8 pawns, 2 bishops, 2 rooks, 2 knights

Total ways of arranging these 16 pieces in 16 boxes

=  16!  =  16!
(8! 2! 2! 2!) (8 × 8!)

Ways of correct arrangement = 1
 
Probability of correct arrangement =  1
(16! / (8 × 8!)

=  (8 × 8!)  =  8!
16! (2 × 15!)

Hence, option B is correct..
5
A child paints the six faces of a cube with six different colors red, blue, pink, yellow, green and orange. What is the probability that red, pink and blue faces share a common corner?
» Explain it
D
We fix the red face and to its left pink face and bottom face as blue 
 
The number of ways to arrange the other three colors = 3!
 
Total ways of painting the six colors
 
First we fix any one color on any one face, let’s say red color.
 
The number of ways five color can be painted = 5!


 
Eliminating the repeated possibilities =  5!  = 5 × 3!
4

We divide by four to eliminate the repeated possibilities as shown in the figure below. These possibilities are counted as different but don’t give us a different arrangement. The arrangement in all four is same.

Probability (Red, pink and blue share a common corner)
=  3!  =  1
5 × 3! 5

Hence, option D is correct.
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Probability is a fundamental concept in math and statistics and deals with the likelihood of an event to occur.

It can range from 0 to 1, where 0 means impossible to occur and 1 indicates a certain event. The probability theory is aimed to find out about how likely events will happen.

To get a grasp over the topic, you can practice daily questions at Smartkeeda. This will help you get better at a topic and improve your time management skills.

The explanation provided at Smartkeeda is in-depth and will help you learn all the essentials of Probability. This is often a dreaded section, but with regular practice, you will be able to solve the questions.

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