Two dice are rolled. What is the probability that the total score is a prime number?

Given :

Two dice are rolled.

To do :

We have to find the probability of getting a total score is a prime number.

Solution :
 

When two dices are rolled, the possible outcomes are,

{(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)}

Tota score should be a prime number means, for example, $(1,1) \Rightarrow 1+1=2$.

2 is a prime number.

The possible outcomes of which total score is prime are,

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

The probability of getting a total score is prime $=  \frac{Number of favorable outcomes}{Tota number of outcomes}$

                                                                                    $=\frac{15}{36}$

Therefore, the probability of getting a total score is prime is $\frac{15}{36}$.

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Updated on: 10-Oct-2022

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