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

a) The probability that 4 randomly selected Americans are all affected by dyslexia is 0.00630441. b) The probability that none of the 4 randomly selected Americans are affected by dyslexia is 0.99369559. c) The probability that at least one of the 4 randomly selected Americans is affected by dyslexia is 0.00630441.

Step-by-step explanation:

a) To find the probability that 4 randomly selected Americans are all affected by dyslexia, we need to multiply the individual probabilities together. The probability of one person being affected by dyslexia is 17.9%, so the probability of four people all having dyslexia is (0.179)^4 = 0.00630441.

b) The probability that none of the 4 randomly selected Americans are affected by dyslexia is the complement of the probability that all 4 have dyslexia. So the probability is 1 - 0.00630441 = 0.99369559.

c) To find the probability that at least one of the 4 randomly selected Americans is affected by dyslexia, we can use the complement rule. The probability that none of the 4 have dyslexia is 0.99369559, so the probability that at least one has dyslexia is 1 - 0.99369559 = 0.00630441.