Question

1. If two dice are thrown simultaneously then the probability of getting a prime
number on both dice is ...
(A) 5/8
(B)2/9
(C)1/3
(D)1/4
​

Answer 1

Step-by-step explanation:

Number in the dice = 1,2 3,4,5,6

No of prime numbers = 2,3,5

( three prime numbers)

$\frac{no \: of \: outcome} = 3 \\ {total \: outcome} = 6$

$\frac{3}{6} = \frac{1}{2}$

Answer 2

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

(i)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

(ii)Favorable outcomes for total of atleast 10 are

(4,6),(5,5),(5,6),(6,4),(6,5),(6,6)

Number of favorable outcomes =6

Hence, the probability of getting a total of atleast 10 = 6/36

= 1/6

(iii)Favorable outcomes for a doublet of even number are

(2,2),(4,4),(6,6)

Number of favorable outcomes =3

Hence, the probability of getting a doublet of even number = 3/36

= 1 /13

(iv)Favorable outcomes for a multiple of 2 on one dice and a multiple of 3 on the other dice are

(2,3),(2,6),(3,2),(3,4),(3,6),(4,3),(4,6),(6,2),(6,3),(6,4),(6,6)

Number of favorable outcomes =11

Hence, the probability of getting a multiple of 2 on one dice and a multiple of 3 on the other dice = 11/36

(v)Favorable outcomes for getting a multiple of 3 as the sum

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

Number of favorable outcomes =12

Hence, the probability of getting a multipleof 3 as the sum 12/30

= 1/3

Step-by-step explanation:

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