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?
Accepted Solution
A:
Answer:0.7569, 0.5729,0.4371Step-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 = pX - 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=[tex]P(X=2) = 0.87^2 = \\0.7569[/tex]b) Here n =4 with same p.[tex]P(X=4) =0.87^4 \\= 0.5729[/tex]c) Prob atleast one is non dash fiction =[tex]P(X< 4)\\= 1-P(X=4)\\=1-0.87^4\\=0.4371[/tex]This is not unusual since 0.4371 probability is not nearer to 0 it is almost half.