What is the probability of having 2 girls in 5 births?

Question

What is the probability of having 2 girls in 5 births?

Answer 1

Let X be the number of girls in five births.  X has the binomial distribution with n = 5 trials and success probability, assuming equally likely to have a male or female offspring, p = 0.5



In general, if X has the binomial distribution with n trials and a success probability of p then

P[X = x] = n!/(x!(n-x)!) * p^x * (1-p)^(n-x)

for values of x = 0, 1, 2, ..., n

P[X = x] = 0 for any other value of x.

The probability mass function is derived by looking at the number of combination of x objects chosen from n objects and then a total of x success and n - x failures.

Or, in other words, the binomial is the sum of n independent and identically distributed Bernoulli trials.

X ~ Binomial( n = 5 , p = 0.5 )

the mean of the binomial distribution is n * p = 2.5

the variance of the binomial distribution is n * p * (1 - p) = 1.25

the standard deviation is the square root of the variance = √ ( n * p * (1 - p)) = 1.118034

The Probability Mass Function, PMF,

f(X) = P(X = x) is:

P( X =  0 ) =  0.03125

P( X =  1 ) =  0.15625

P( X =  2 ) =  0.3125

P( X =  3 ) =  0.3125

P( X =  4 ) =  0.15625

P( X =  5 ) =  0.03125

Answer 2

each time you give birth is like flipping a coin. it's a 50-50 chance

it's possible to give birth 5 times and have all boys. blame the father for his Y chromosome

Answer 3

anyone who has 5 kids in this day and age is nuts...

you have 50/ 50 each time..

I would say a 1 in 16 chance...

Answer 4

2 over 5

Answer 5

2/5

Answer 6

it's simple 2/5