Question

According to the National Vital Statistics Report, Vol. 52, No. 10, the probability is 0.6591 that a newborn baby has a birth weight between 6 lbs, 10 oz. and 8 lbs, 13 oz. If 2 newborn babies are randomly selected, what is the probability that at least one of the babies has a birth weight between 6 lbs, 10 oz. and 8 lbs, 13 oz.? Assume birth weights of different babies are independent. (use 3 decimal places in your answer)

Answer 1

Probability that at least one of the babies has the specified birth weight is

Probability(1st baby has a birth weight between 6 lbs, 10 oz. and 8 lbs, 13 oz and 2nd baby does not have) +

Probability(2nd baby has a birth weight between 6 lbs, 10 oz. and 8 lbs, 13 oz and 1st baby does not have) +

Probability(both the babies have a birth weight between 6 lbs, 10 oz. and 8 lbs, 13 oz)

=0.6591*(1-0.6591)+0.6591*(1-0.6591)+(0.6591*0.6591)

=0.88378719(Ans)

Reason-Birth weights of different babies are independent.Hence,one baby of a specified birth weight does not influence other babies.Any two randomly chosen babies can have any birth weight.