**Probability Questions and Answers – Download PDF!!!. **Probability theory had start in the 17th century. It is one of the branches in mathematics. The probability value is expressed from 0 to 1.Classical, Relative, Subjective are the types of probability. Here some Probability question is explained with solutions.

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__Probability – Easy__

__Probability – Easy__

**There are 15 boys and 10 girls in a class. If three students are selected at random, what is the probability that 1 girl and 2 boys are selected?**

A. 1/40

B. 1/ 2

C. 21/46

D. 7/ 41

E. None of these

**Correct option is : C**

**Solution:**

Total number of ways of selecting 3 students from 25 students = ^{25}C_{3}

Number of ways of selecting 1 girl and 2 boys = selecting 2 boys from 15 boys and 1 girl from 10 girls

⇒ Number of ways in which this can be done = ^{15}C_{2} × ^{10}C_{1}

⇒ Required probability = (^{15}C_{2} × ^{10}C_{1})/ (^{25}C_{3})

**Two friends Harish and Kalyan appeared for an exam. Let A be the event that Harish is selected and B is the event that Kalyan is selected. The probability of A is 2/5 and that of B is 3/7. Find the probability that both of them are selected.**

A. 35/36

B. 5/35

C. 5/12

D. 6/35

E. None of these

**Correct option is : D**

**Solution:**

Given, A be the event that Harish is selected and

B is the event that Kalyan is selected.

P(A)= 2/5

P(B)=3/7

Let C be the event that both are selected.

P(C)=P(A)×P(B) as A and B are independent events:

P(C) = 2/5*3/7

P(C) =6/35

The probability that both of them are selected is 6/35

**A card is drawn from a well shuffled pack of 52 cards. What is the probability of getting queen or club card?**

A. 17/52

B. 15/52

C. 4/13

D. 3/13

E. None of these

**Correct option is : C**

**Solution:**

The probability of getting queen card = 4/52

The probability of getting club card = 13/52

The club card contains already a queen card, therefore required probability is,

4/52 + 13/52 – 1/52 = 16/52 = 4/13

**16 persons shake hands with one another in a party. How many shake hands took place?**

A. 124

B. 120

C. 165

D. 150

E. None of these

**Correct option is : B**

**Solution:**

Total possible ways = ^{16}C_{2}

= 120

**2 dice are thrown simultaneously. What is the probability that the sum of the numbers on the faces is divisible by either 3 or 5?**

A. 7/36

B. 19/36

C. 9/36

D. 2/7

E. None of these

5. **Correct option is : B**

**Solution:**

Clearly n(s) = 6*6 = 36

Let E be the event that the sum of the numbers on the 2 faces is divisible by either 3 or 5. Then

E = {(1,2), (1,4), (1,5), (2,1), (2,3), (2,4), (3,2), (3,3), (3,6), (4,1), (4,2), (4,5), (4,6), (5,1), (5,4), (5,5), (6,3), (6,4), (6,6)}

n(E) = 19

Hence P(E) = n(E) / n(s)

= 19/ 36

__Probability – Moderate__

__Probability – Moderate__

**Daniel speaks truth in 2/5 cases and Sherin lies in 3/7cases. What is the percentage of cases in which both Daniel and Sherin contradict each other in stating a fact?**

A. 72.6%

B. 51.4%

C. 62.3%

D. 47.5%

E. None of these

**Correct option is : B**

**Solution:**

Daniel and Sherin will contradict each other when one speaks truth and other speaks lies.

Probability of Daniel speak truth and Sherin lies

=2/5*3/7

=6/35

Probability of Sherin speak truth and Daniel lies

=4/7*3/5

=12/35

The two probabilities are mutually exclusive.

Hence, probabilities that Daniel and Sherin contradict each other:

=6/35 +12/35

=18/35

=18/35*100

=51.4%

**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?**

A. 1/18

B. 1/15

C. 1/6

D. 1/12

E. None of these

**Correct option is : C**

**Solution:**

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

**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?**

A. 95/102

B. 19/23

C. 21/26

D. 46/51

E. None of these

**Correct option is : D**

**Solution:**

Number of ways in which the person can pick three balls out of 18 balls

= ^{18}C_{3} = 816

Number of ways of picking 3 balls of same colour = ^{6}C_{3}+ ^{4}C_{3 }+ ^{8}C_{3} = (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 |

**Bag A contains 3 green and 7 blue balls. While bag B contains 10 green and 5 blue balls. If one ball is drawn from each bag, what is the probability that both are green?**

A. 29/30

B. 1/5

C. 1/3

D. 1/30

E. None of these

4. **Correct option is : B**

**Solution:**

The required probability = ^{3}C_{1}/^{10}C_{1} × ^{10}C_{1}/^{15}C_{1}

= 3/10 × 10/15 = 1/5

**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?**

A. 8!/16!

B. 8!/(2*15!)

C. 8!/15!

D. (2*8!)/16!

E. None of these

**Correct option is : B**

**Solution:**

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!) |

** **

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