Question

19. In two dice game, the player take turns to roll both dlce, they can roll
as many times as they want in one turn. A player scores the sum of the
two dice thrown and gradually reaches a higher score as they continue to
roll. If a single number 1 is thrown on either dio, the score for that whole
turn is lost. Two dice are thrown simultaneously.
(1) What is the probability of getting the sum as an even number?
(A) 4 (B) (C) 14 (D) 5/8
(2) What is the probability of getting the sum as a prime number?
(A) 5/12 (B) 1/6
(C) 7/12 (D) 11/12
(3) What is the probability of getting the sum of atleast10?
(A) 5/12
(B) 5/6 (C) 1/6 (D) 7/12
(4) What is the probability of getting a doublet of even number?
(A)1/12
(B) 5/12 (C) 11/12 (D) 7/12
(5) What is the probability of getting a product of numbers greater than 16?
(A) 7/36 (B) 2/9 (C) 1/1 (D) 11/36
5 of 9​

Answer 1

Answer:

Explanation:Let's number all the throws of the die.

A can win only in odd throws, which are of the form (2i+1).

P(A wins) = ∑∞i=0P(A wins in the (2i+1)th throw)

because these events are mutually exclusive.

Note that the term corresponding to i=0 has value zero.

For other terms, we can write:

P(A wins in the (2i+1)th throw)

=P(a1+a2≠7)P(a2+a3≠7)...P(a2i−1+a2i≠7)P(a2i+a2i+1=7)

where aj is the number obtained in the jth throw.