Question

An unbiased die is rolled twice. Find the probability of getting (i) the sum of two numbers as a prime (ii) the sum of two numbers equal to 9

Answer 1

Answer:

see, its sample space will contain 36 possibilities

since, 6*6=36

means there are 36 different pairs

Step-by-step explanation:

now pairs that will give sum as prime no. is (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)

probability will be 5/12.

2) P(getting sum as 9) = 1/9

Answer 2

Given:

Number of dice rolled = 1.

To Find:

We are asked to find the Probability of getting (i) the sum of two numbers as prime.  (ii) the sum of two numbers equal to 9

Solution:

Given the number of dice rolled = 1

total number of outcomes = 36

Number of times rolled = 2

(i) The sum of two numbers as prime

Number of pairs by which we get the sum of two number as prime are

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

Probability of getting sum of two numbers as prime,

$P(E)= \frac{number of favourable outcomes}{total number of outcomes}=\frac{15}{36}=\frac{5}{12}$

(ii) The sum of two numbers equal to 9

Number of pairs by which we get the sum of two number equal to 9 are

(4,5),(5,4),(6,3),(3,6)

probability of getting sum of two number equal to 9,

$P(E)= \frac{4}{36}=\frac{1}{9}$

Hence the sum of two number as a prime is $\frac{5}{12}$ and sum of two number equal to 9 is $\frac{1}{9}$

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