Question

Two dice are thrown simultaneously. Find the probability of the following events.
(i) The sum of the digits on the upper faces is at least 8.
(ii) The product of the digits on the upper faces is 12.​

Answer 1

Answer:

Two dice are thrown simultaneously. Find the probability of the following events.

(i) The sum of the digits on the upper faces is at least 8.

(ii) The product of the digits on the upper faces is 12.

Step-by-step explanation:

call

8011141183

now

Answer 2

Answer:

$$ \begin{array}{l}Sample \ space (s)=\left\{(1,1)(1,2)(1,3)(1,4)(1,5)(1,6) \\ (2,1)(2,2)(2,3)(2,4)(2,5)(2,6) \\ (3,1)(3,2)(3,3)(3,4)(3,5)(3,6) \\ (4,1)(4,2)(4,3)(4,4)(4,5)(4,6) \\ (5,1)(5,2)(5,3)(5,4)(5,5)(5,6) \\ (6,1)(6,2)(6,3)(6,4)(6,5)(6,6)\right\} \end{array} $$

∴n(S)=36

Event A: sum of the digits on the upper faces is at least 10A={(4,6),(5,5),(5,6),(6,4),(6,5),(6,6)}

∴n(A)=6

∴P(A)=

n(S)

n(A)

=

36

6

=

6

1

Hence, the probability that the sum of the digits on the upper faces is at least 10 is =

6

1

Step-by-step explanation:

$$ \begin{array}{l}Sample \ space (s)=\left\{(1,1)(1,2)(1,3)(1,4)(1,5)(1,6) \\ (2,1)(2,2)(2,3)(2,4)(2,5)(2,6) \\ (3,1)(3,2)(3,3)(3,4)(3,5)(3,6) \\ (4,1)(4,2)(4,3)(4,4)(4,5)(4,6) \\ (5,1)(5,2)(5,3)(5,4)(5,5)(5,6) \\ (6,1)(6,2)(6,3)(6,4)(6,5)(6,6)\right\} \end{array} $$

∴n(S)=36

Event A: sum of the digits on the upper faces is at least 10A={(4,6),(5,5),(5,6),(6,4),(6,5),(6,6)}

∴n(A)=6

∴P(A)=

n(S)

n(A)

=

36

6

=

6

1

Hence, the probability that the sum of the digits on the upper faces is at least 10 is =

6

1