**Maharashtra Board Class 10 Math Part – 1 Solution Chapter 5 Practice Set 5.3 – Probability**

Balbharati Maharashtra Board Class 10 Math Part – 1 Solution Chapter 5: Probability. Marathi or English Medium Students of Class 10 get here Probability full Exercise Solution.

Std |
Maharashtra Class 10 |

Subject |
Math Part 1 Solution |

Chapter |
Probability |

Practice Set |
5.3 |

__Practice Set – 5.3__

__Practice Set – 5.3__

**(1) Write sample space ‘S’ and number of sample point n(S) for each of the following experiments. Also write events A, B, C in the set form and write n(A), n(B), n(C).**

**(1) One die is rolled,**

** Event A: Even number on the upper face.**

** Event B: Odd number on the upper face.**

** Event C: Prime number on the upper face.**

**Solution: **

One die is rolled.

S = {1, 2, 3, 4, 5, 6}, n(s) = 6.

For event A:

A = {2, 4, 6} n(A) = 3

For event B:

B = {1, 3, 5} n(B) = 3

For event C:

C = {3, 2, 3, 5} n(C) = 3

** **

**(2) Two dice are rolled simultaneously,**

** Event A: The sum of the digits on upper faces is a multiple of 6.**

** Event B: The sum of the digits on the upper faces is minimum 10.**

** Event C: The same digit on both the upper faces.**

**Solution: **

Two dies are rolled

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

n(s) = 36

For event A:

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

n(A) = 6

For event B:

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

n (B) = 33

For event C:

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

n (C) = 6

** **

**(3) Three coins are tossed simultaneously.**

**Condition for event A: To get at least two heads.**

**Condition for event B: To get no head.**

**Condition for event C: To get head on the second coin. **

**Solution: **

3 coin tossed simultaneously.

S {HHH, HHT, HTT, HTH, TTT, TTH, THH, THT}

n (s) = 8

For event A:

A = {HHH, HHT, HTH, THH}

n (A) = 4

For event B:

B = {TTT}

n (n) = 1

For even C:

C = {HHH, HHT, THH, THT}

n(c) = 4

** **

**(4) Two digit numbers are formed using digits 0, 1, 2, 3, 4, 5 without repetition of the digits.**

**Condition for event A: The number formed is even**

**Condition for event B: The number formed is divisible by 3.**

** Condition for event C: The number formed is greater than 50.**

**Solution: **

Two digit number formed using 0, 1, 2, 3, 4, 5. Without-repetition.

S = {10, 12, 13, 14, 15, 20, 21, 23, 24, 25, 30, 31, 32, 34, 35, 40, 41, 42, 43, 45, 50, 51, 52, 53, 54}

n (s) = 25

For event – A:

A = {10, 12, 14, 20, 24, 30, 32, 34, 40, 42, 50, 52, 54}

n (A) = 13

For even B:

B = {12, 15, 21, 24, 30, 42, 45, 51, 54}

n (B) = 9

For event C:

C = {51, 52, 53, 54}

n (c) = 4

** **

**(5) From three men and two women, environment committee of two persons is to be formed.**

**Condition for event A: There must be at least one woman member.**

**Condition for event B: One man, one woman committee to be formed.**

**Condition for event C: There should not be a woman member.**

**Solution: **

From 3 men two women environment committee of two person is formed.

Let, 3 men be M_{1}, M_{2}, M_{3}

2 women be w_{1}, w_{2}

∴ S = {M_{1}, M_{2}), (M_{1}, M_{3}), (M_{1}, W_{1}), (M_{1}, W_{2}), (M_{2}, M_{3}), (M_{2}, W_{1}), (M_{3}, W_{1}), (M_{2}, W_{2}), (W_{1}, W_{2})}

n(s) = 10

For event A:

A {(M_{1}, W_{1}), (M_{1}, W_{2}), (M_{2}, W_{1}), (M_{2}, W_{2}), (M_{3}, W_{1}), (M_{3}, W_{2}), (W_{1}, W_{2})

n (A) = 7

For event B:

B = {(M_{1}, W_{1}), (M_{1}, W_{2}), (M_{2}, W_{1}), (M_{2}, W_{2}), (M_{3}, W_{1}), (M_{3}, W_{2})

n (B) = 6

For event c:

C = {(M_{1}, M_{2}), (M_{1}, M_{3}), (M_{2}, M_{3})}

n (c) = 3

** **

**(6) One coin and one die are thrown simultaneously.**

**Condition for event A: To get head and an odd number.**

**Condition for event B: To get a head or tail and an even number.**

**Condition for event C: Number on the upper face is greater than 7 and tail on the coin.**

**Solution: **

One coin and die thrown.

∴ S {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}

n (s) = 12

For event A:

A = {(H, 1), (H, 3), (H, 5)}

n (A) = 3

For event B:

B = {(H, 2), (H, 4), (H, 6), (T, 2), (T, 4), (T, 6)}

n (B) = 6

For event C:

C = {Not possible}

n (C) = 0

**Here is your solution of Maharashtra Board Class 10 Math Part – 1 Chapter 5 Probability Practice Set 5.3 Solution**

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