Question

5. A pair of dice is tossed simultaneously. Find
the probability that the sum of numbers on
the dice is a prime number.​

Answer 1

Answer:

Sample space for total number of possible outcomes

(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)

Total number of outcomes =36

Favorable outcomes for sum as prime are

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

Number of favorable outcomes =15

Hence, the probability of getting the sum as a prime number. = 15/36 = 5/12.

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Answer 2

Answer:

1/2 for one dice and 5/12 for 2 duce

Step-by-step explanation:

Numbers on the 1 Dice = 6

Prime numbers are = 2,3,5

Numbers on the 2 Dice = 12

Prime numbers are = 2,3,5,7,11