Question

3. Two dice are rolled. What’s the conditional probability that both dice are 5’s if it’s known that the sum of points is divisible by 5?

Answer 1

Answer:

$Pr =\frac{1}{3}$

Step-by-step explanation:

Given

$S = \{(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)$

$(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)$

$(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)\}$ --- sample space

First, list out all outcomes whose sum is divisible by 5

$A = \{(4,6), (5,5),(6,4)\}$

So, we have:

$n(A) = 3$

Next, list out all outcomes that has an outcome of 5 in both rolls

$B = \{(5,5)\}$

$n(B) =1$

The required conditional probability is:

$Pr =\frac{n(B)}{n(A)}$

$Pr =\frac{1}{3}$