Question

A pair of dice is thrown twice .Find the Probability of scoring 7 points

i) once
ii) twice and
iii) atleast once

Using binomial distribution

Answer 1

The probability of scoring 7 points on a pair of dice thrown twice is 10/36 for once, 1/36 for twice, and 11/36 for at least once using binomial distribution.

Step-by-step explanation:

The probability of scoring 7 points with a pair of six-sided dice in one throw is 6/36, since there are 6 favorable outcomes (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) out of 36 possible outcomes.


For two throws, we can use the binomial distribution with n=2 trials, the probability of success on a single trial p=1/6, and the probability of failure q=5/6.

1. Probability of scoring 7 points exactly once: This is the probability of one success and one failure in either order.
   Using the formula for the binomial probability, P(X=k) = (n choose k) * p^k * q^(n-k), we get P(X=1) = (2 choose 1) * (1/6)^1 * (5/6)^1 = 2 * 1/6 * 5/6 = 10/36.
   
   
2. Probability of scoring 7 points twice: This is the probability of two successes. Using the same binomial probability formula, we get P(X=2) = (2 choose 2) * (1/6)^2 * (5/6)^0 = 1/36.
   
   
3. Probability of scoring 7 points at least once: This can be found by subtracting the probability of no successes from 1. P(X≥1) = 1 - P(X=0) = 1 - (2 choose 0) * (1/6)^0 * (5/6)^2 = 1 - (5/6)^2 = 1 - 25/36 = 11/36.