We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

On the morning of January 1, a hospital nursery has 3 boys and some number of girls. That night, a woman gives birth to a child, and that child is placed in the nursery.

On January 2, a statistician conducts a survey and selects a child at random from the nursery. The child happens to be a boy. What is the probability the child born on January 1 was a boy? Thanks for this.

Guest May 30, 2017

#2**0 **

According to our teacher, the answer is 4/7, not 1/2 but have no idea how he gets that.

Guest May 31, 2017

#3**+1 **

Assume there are g number of girls. So we have a total of: g+3 children. The newly-born child has a 50% chance of being a boy, in which case will have: g+4 children. It also has a 50% chance of being a girl, in which case will have: g+1+3=g+4 children.

Then the probability of selecting a boy and the newly-born child is a boy is: 4/[g+4]*1/2.

The probability of selecting a boy and the newly-born child is a girl is: 3/[g+4]*1/2.

Then the probability of selecting a boy =4/[g+4]*1/2 + 3/[g+4]*1/2 =3.5/[g+4].

Finally, the probability of being born a boy, given the probability of selecting a boy(calculated above) is: {4/[g+4]*1/2} / {3.5/[g+4]} =2/3.5 =4/7.

Guest May 31, 2017