Question

If a couple plans to have 6 ​children, what is the probability that there will be at least one boy​? Assume boys and girls are equally likely. Is that probability high enough for the couple to be very confident that they will get at least one boy in 6 ​children?

Answer 1

Answer:

a) $\frac{63}{64}$

b) The probability for the couple to be very confident that they will get at least one boy in 6 ​children is $98.43$%

Step-by-step explanation:

The probability of having a boy or girl is $0.5$

A couple plans to have 6 children

Probability of having at least one male child

$1- (0.5)^6$

On solving the above term, we get -

$1- (\frac{1}{2})^6\\= 1-\frac{1}{64}\\ = \frac{63}{64}$

The probability for the couple to be very confident that they will get at least one boy in 6 ​children is

$\frac{63}{64}* 100\\ = 98.43$

Thus, the probability is very high