Question

A book can be classified as either non dash fiction or fiction. Suppose that 87​% of books are classified as fiction. ​(a) Two books are chosen at random. What is the probability that both books are fiction​? ​(b) Four books are chosen at random. What is the probability that all four books are fiction​? ​(c) What is the probability that at least one of four randomly selected books is non dash fiction​? Would it be unusual that at least one of four randomly selected books is non dash fiction​?

Answer 1

Answer:

0.7569, 0.5729,0.4371

Step-by-step explanation:

Given that the books are of only two types either non dash fiction or fiction.

Also probability of selecting a fiction = 0.87 = p

X - no of books fiction selected is binomial with p = 0.87 and n =2

(since each trial is independent of the other and there are only two trials)

a) the probability that both books are fiction=

$P(X=2) = 0.87^2 = \\0.7569$

b) Here n =4 with same p.

$P(X=4) =0.87^4 \\= 0.5729$

c) Prob atleast one is non dash  fiction =$P(X< 4)\\= 1-P(X=4)\\=1-0.87^4\\=0.4371$

This is not unusual since 0.4371 probability is not nearer to 0 it is almost half.