Question

According to the a study in a psychology journal, 17.9% of Americans are affected by dyslexia. You do not have to round, but you may round your answers to 4 decimal places.

a) What is the probability that 4 randomly selected Americans are all affected by dyslexia?

b) What is the probability that none of the 4 randomly selected Americans are affected by dyslexia?

c) What is the probability that at least one of the 4 randomly selected Americans is affected by dyslexia?

Answer 1

For part a, the probability that 4 randomly selected Americans are all affected by dyslexia is 0.0024.

For part b, the probability that none of the 4 randomly selected Americans are affected by dyslexia is 0.6246

For part c, the probability that at least one of the 4 randomly selected Americans is affected by dyslexia is 0.3754.

Step-by-step explanation:

To calculate the probabilities, we can use the binomial probability formula:

P(X=k) = C(n, k) * p^k * (1-p)^(n-k)

where:

n is the number of trials (in this case, 4)

k is the number of successes (in this case, 4 for part a, 0 for part b, and at least 1 for part c)

p is the probability of success (in this case, 17.9% or 0.179)

For part a):

P(X=4) = C(4, 4) * 0.179^4 * (1-0.179)^(4-4)

= 0.0024247

For part b):

P(X=0) = C(4, 0) * 0.179^0 * (1-0.179)^(4-0)

= 0.6246059

For part c):

P(X>=1) = 1 - P(X=0)

= 1 - 0.6246059

= 0.3753941