Probability?

Question

If a couple plans on having four children. What is the probability that one will be a girl?

How do I figure this out?

Answer 1

assuming that the sex of the child is completly random and that there is an equal probability that the child is either a boy or girl ie 1/2.

Then its just the probability that there is one girl and 3 boys, so P(1 girl) = 0.5 X (0.5)^3

Acutally you would then multiply this figure by 4 becuase there are 4 outcomes: GBBB, BGBB, BBGB, BBBG

You could use the binomial probability formula where:

P(1 girl) = nCr X p^r X q^(n-r) where nCr can be found on ue calculator, p=prob of girl, q = prob of boy

Hence for our case:

P(1 Girl) = 4C1 X 0.5 X 0.5^3 = 0.0625

Answer 2

The probability of not having a girl is (1/2)^4 = 1/16
Therefore the probability of a girl is 15/16 , approx 94%

Answer 3

if you have 1 child, it could be a boy or a girl, so having a girl is a 1/2 ratio. the next one will be a boy or a girl, so that is 1/2. if you multiply 1/2 x 1/2 x 1/2 x 1/2, because they are having 4 children, and the probability of having a girl is 1/2, you get 1/16 or one sixteenth.
hope that helps!

Answer 4

You can do a Punnett Square. MM for male and mm for female. You will see out of four half will be mm, which means girls. The probability is 1/2 for a girl and boy.

Answer 5

The probability at each birth is 50% (In reality not quite)

If there is to be ONLY one girl, there are four options

BBBG
BBGB
BGBB
GBBB

each of these outcomes has a probablilty of 0.5*0.5*0.5*0.5=0.0625 as there are four possible scenarios, the probability of EXACTLY one girl is 0.0625 *4= 0.25

The probablilty of AT LEAST 1 girl is 1- (prob of BBBB)

BBBB prob = 0.0625

So The probablilty of AT LEAST 1 girl is 1- (prob of BBBB)
= 1-0.0625
= 0.9375
= 93.75%

Answer 6

Hi there,
The probability will be 1 - P(None are girls) = 1 - P(All are boys) = 1 - (.5)^4 = 0.9375.