Question

Two dice are rolled. Find the probability for the following events:

(a) Event A: The sum of digits on the upper faces is at least 6.

(b) Event B: The sum of the digits on the upper faces is 13.

(c) Event C: The sum of the digits on the upper faces is divisible by 5.

(d) Event D: The sum of the digits on the upper faces is at most 6.


please answer it​

Answer 1

Answer:

Two dice are thrown

∴ 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)}

∴n(S)=36

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

n(A)=6

Probability, P(A)=

n(S)

n(A)

=

36

6

=

6

1

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

n(B)=7

Probability, P(B)=

n(S)

n(B)

=

36

7

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

n(C)=15

Probability, P(C)=

n(5)

n(C)

=

36

15