Question

find the probability of getting a sum of 7 or 8 in throwing a die twice

Answer 1

Probability of getting sum of 7 or 8 is $\bold{\frac{11}{36}}$ when the dice is thrown twice.

Solution:

The total possibility of numbers when throwing 2 dices is used as Sample Space for the problem:  $36 = 6 \times 6$

Possible combination of 2 dices casted is {1,2,3,4,5,6} and {1,2,3,4,5,6}

Possibility for sum 7 on the 2 dies casted  = 6  [{1,6}{2,5}{3,4}{4,3}{5,2}{6,1}]

Possibility for sum 8 on the 2 dies casted  = 5 [{2,6}{3,5}{4,4}{5,3}{6,2}]

The possibility of getting 7 or 8 when the dies are casted = 6+5 = 11

Total probability of getting a sum of 7 or 8 = $\bold{\frac{11}{36}}$.  

Answer 2

The probability of getting a sum of 7 or 8 in throwing a die twice is $\frac{11}{36}$

Step-by-step explanation:

Given Data

Total number of outcomes n(S) = 36

To find the probability of getting a sum of 7 or 8 in throwing a die twice

Possibilities in getting a sum of 7  = (1,6) , (2,5) , (3,4) , (4,3) , (5,2) and (6,1)

Number of possibilities in getting a sum of 7, n(A) = 6

Possibilities in getting a sum of 8 = (2,6) , (3,5) , (4,4) , (5,3) and (6,2)

Number of possibilities in getting a sum of 8, n(B) = 5

$\text {Probability of getting sum of 7 or 8} = \frac{\text{Number of possibilities of getting 7 or 8}}{\text{Total number of outcomes}}$

Probability of getting sum of 7 or 8 = P(A) + P(B)

$\text {Probability of getting a sum of 7 or 8} = \frac{n(A)}{n(S)} + \frac{n(B)}{n(S)}$

$\text {Probability of getting a sum of 7 or 8} = [ \frac{6}{36} + \frac{5}{36} ]$

$\text {Probability of getting a sum of 7 or 8} = \frac{11}{36}$

Therefore the probability of getting sum of 7 or 8 in throwing a die twice is $\frac{11}{36}$

To Learn More ...

1) A die is thrown twice. what is the probability of the events (getting a doublet)

https://brainly.in/question/2427508

2) A die is thrown twice. What is the probability that (i) 5 will not come up either time? (ii) 5 will come up at least once?

[Hint : Throwing a die twice and throwing two dice simultaneously are treated as the same experiment].

https://brainly.in/question/4918347