The odds that a book will be favourably reviewed by three
independent critics are 5 to 2, 4 to 3 and 2 to 3 respectively.
Odds of 5 to 2 means that on the average, out of 5+2=7 times a
book is reviewed, a book will be favorably reviewed 5 times
and unfavorably 2 times. So the probability that it will be
reviews favorably is 5 times out of 7 or 5/7.
Odds of 4 to 3 means that on the average, out of 4+3=7 times a
book is reviewed, a book will be favorably reviewed 4 times
and unfavorably 3 times. So the probability that it will be
reviews favorably is 4 times out of 7 or 4/7.
Odds of 2 to 3 means that on the average, out of 2+3=5 times a
book is reviewed, a book will be favorably reviewed 2 times
and unfavorably 5 times. So the probability that it will be
reviews favorably is 2 times out of 5 or 2/5.
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What is the probability that of three reviews a majority will be
favourable?The probability of 1 book being favorably reviewed by all 3 critics
is the product of the probabilities (5/7)(4/7)(2/5) = 8/49.
Edwin
