Question

If I roll two dice, what is the probability that both of them are both prime and even?

Answer 1

Answer:

When two dice are thrown we get outcome as

[ (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) ]

Therefore sample space is equal to 36

Now prime no. between 1–6 are 2, 3 and 5 and favorable outcome on both dices will be

[ (2,2),(2,3),(2,5),(3,2),(3,3),(3,5),(5,2),(5,3),(5,5) ]

it means that favorable outcome is 9

Now probability = total favorable outcome/ sample space

that is 9/36

= 1/4 or 0.25

Hence probability of getting a prime number on both dice is 1/4.

Step-by-step explanation:

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