Question

Two dice are thrown simultaneously .Find the probability of getting

(A) A total of at least 10

(B) The sum as a prime number

Answer 1

Answer:

A) $\text{Probability}=\frac{1}{6}$

B) $\text{Probability}=\frac{5}{12}$

Step-by-step explanation:

Given : Two dices are thrown simultaneously.

To find : The probability of getting

(A) A total of at least 10

(B) The sum as a prime number

Solution :  

When two dice rolled once the outcome will be,

(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)  

Now,  

$\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total number of outcome}}$

(A) A total of at least 10

Favorable outcome are :  (4,6),  (5,5), (5,6), (6,4), (6,5), (6,6)  

So, Number of favorable outcome = 6

Total number of outcome = 36

$\text{Probability}=\frac{6}{36}$

$\text{Probability}=\frac{1}{6}$

(B) The sum as a prime number

Favorable outcome 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)

So, Number of favorable outcome = 15

Total number of outcome = 36

$\text{Probability}=\frac{15}{36}$

$\text{Probability}=\frac{5}{12}$

Answer 2

(A) $\frac{1}{6}$ is the probability of getting  a total of at least 10

(B) $\frac{5}{12}$ is the probability of getting sum as a prime number

Step-by-step explanation:

Given data

To find - the probability of (a) total of at least 10 and the sum as a prime number, when two dice are thrown simultaneously

Probability is defined as the ratio between number of possibilities and total number of terms.

$P(A)=\frac{n(A)}{n(S)}$

Where n(A) - number of possibilities and n(S) = total number of terms

Total number of terms n(S) when two dice are thrown simultaneously are 36

(A) A total of at least 10

The terms which give at least 10 are (4,6), (5,5), (5,6), (6,4), (6,5) and  (6,6)  

For a total of at least 10 number of possibilities are 6

The probability of getting a total of at least 10 is,

$P(A)=\frac{6}{36}$

$P(A) = \frac{1}{6}$

(B) The sum as a prime number

The terms which gives sum as prime number are (1,1), (1,2), (2,1), (2,3), (3,2), (1,4), (4,1), (2,5), (5,2), (1,6), (6,1), (3,4), (4,3), (5,6) and (6,5).

The The number of possibilities getting sum of prime number are 15

n(B) = 15

$P(B)=\frac{15}{36}$

$P(B)=\frac{5}{12}$

Therefore the probability of getting a total of at least 10 is $\frac{1}{6}$ and the probability of getting sum as prime number is $\frac{5}{12}$, when two dice are thrown simultaneously.

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