Question

Two dice are thrown simultaneously .find the probability the sum of the numbers appears on dice is 5 , if the number of first dice is 4 always.
1. 3/6
2. 1/6
3. 7/6
4. 1/7
5. 2/3

Answer 1

Correct Answer - Option 2 : 1/6

Given

Two sides are thrown

Concept

Multiplication theorem on probability

If A and B are two events associated with a random experiment, then

P(A.  B) = P(A) .P(B/A)

Calculation

Let A is the event of occurrence of 4 on first dice

⇒ n(A) = 6 i.e[(4,1), (4,2), (4,3), (4,4); (4,6) and (4,5)]

and B is the event of occurrence of such numbers on both dice whose sum is 5 = [(4,1); (3,2); (2,3) and (1,4)]

Thus, A.  B = (4,1)

⇒ n(A B) = 1

P(B/A) = 1/6