Harry Potter books have become popular with children and adults alike. A recent

Question

Harry Potter books have become popular with children and adults alike. A recent survey conducted in London revealed that 74% high school students have read the first Harry Potter book. A random sample of 7 London high school students is taken, and the number of students who have read the first Harry Potter book is recorded.

(Round all probability answers to four decimals)

d) What is the probability that exactly two of the randomly selected students has read the first Harry Potter book?

e) What is the probability that at least two of the randomly selected students have read the first Harry Potter book?

f) What is the probability that no more than five of the randomly selected students have read the first Harry Potter book?

g) What is the probability that between two and seven (inclusive) of the randomly selected students have read the first Harry Potter book?  

h) What is the probability that more than seven of the randomly selected students have read the first Harry Potter book?

Explanation / Answer

d) P(X = 2) = 7C2 * (0.74)^2 * (0.26)^5 = 0.0137

E) P(X > 2) = 1 - P(X < 2) = 1 - (P(X = 0) + P(X = 1) )

= 1 - (7C0 * (0.74)^0 * (0.26)^7 + 7C1 * (0.74)^1 * (0.26)^6) =

= 1- 0.0017= 0.9983

F) P(X < 5) = 1 - P(X > 5) = 1 - (P(X = 5) + P(X = 6) + P(X = 7))

= 1 - (7C5 * (0.74)^5 * (0.36)^2 + 7C6 " (0.74)^6 * (0.26)^1 + 7C7 * (0.74)^7 * (0.26)^0 = 1 - 0.7354 = 0.2646

G) P(2 < X < 7) = P(X = 2) + P(X= 3) + P(X= 4) + P(X = 5) + P(X = 6) + P(X = 7)

= 7C2 * (0.74)^2 * (0.26)^5 + 7C3 * (0.74)^3 * (0.26)^4 + 7C4 * (0.74)^4 * (0.26)^3 + 7C5 * (0.74)^5 * (0.26)^2 + 7C6 * (0.74)^6 * (0.26)^1 + 7C7 * (0.74)^7 * (0.26)^0 = 0.9983

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