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

Answer:

The required probability is 0.884

Step-by-step explanation:

Consider the provided information.

The probability is 0.6591 that a newborn baby has a birth weight between 6 lbs, 10 oz. and 8 lbs, 13 oz.

The probability that weight is not in between  6 lbs, 10 oz. and 8 lbs, 13 oz is:

1-0.6591=0.3409

We want to find the probability that if 2 babies born then the probability that at least one of the babies has a birth weight between 6 lbs, 10 oz. and 8 lbs, 13 oz.

There are 3 possible case

Case I: If only first baby weight is in between 6 lbs, 10 oz. and 8 lbs, 13 oz.

Case II: If only second baby weight is in between 6 lbs, 10 oz. and 8 lbs, 13 oz.

Case III: If both babies weight is in between 6 lbs, 10 oz. and 8 lbs, 13 oz.

This can be written as:

$0.6591 \times 0.3409+0.3409\times 0.6591+0.6591\times 0.6591\approx 0.884$

Hence, the required probability is 0.884