Question

find the probability of 1. 12 successes in 20 trials when the probability of a success is 0.7 2. 8 failures in 20 trials when the probability of a failure is 0.3 3. explain why you get identical answers in parts a and b

thank you

Answer 1

find the probability of

1. 12 successes in 20 trials when the probability of a success is 0.7

p = 0.7

n = 20

r = 12

Probability = ²⁰C₁₂(0.7)¹²(1-0.7)^20-12 = 0.1144

2. 8 failures in 20 trials when the probability of a failure is 0.3

p = 0.3

n = 20

r = 8

Probability = ²⁰C₈(0.3)⁸(1-0.3)^20-8 = 0.1144

3. explain why you get identical answers in parts a and b

We will turn the question 2. for successes:

p = 1 - 0.3 = 0.7

n = 20

r = 20 - 8 = 12

Probability = ²⁰C₁₂(0.7)¹²(1-0.7)^20-12 = 0.1144

The answers are identical because the probability of success and failure are the same.