**(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:**

Given Event A: Even number on the upper face.

Event B: Odd number on the upper face.

Event C: Prime number on the upper face.

Sample space, S = {1, 2, 3, 4, 5, 6}

Number of sample points, n(S) = 6

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

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

C = {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:**

Given 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.

Sample space, 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)}

Number of sample points, n(S) = 36

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

B = {(4, 6) (5, 5) (5, 6) (6, 4) (6, 5) (6, 6)}, n(B) = 6

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:**

Given 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

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

Number of sample points, n(S) = 8

To get at least two heads, A = {HHH, HHT, HTH, THH}

n(A) = 4

To get no head, B = {TTT}

n(B) = 1

To get head on the second coin, C = {HHH, HHT, THH}

n(C) = 3