A family has 3 children. Their first child was a girl. What I'd the probability that the two children are of different gender?
Are you asking for the probability that the other two children are male?
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
Approx. 1/2 * 1/2 = 1/4
The probabilities are not exactly 1/2.
To determine the probability that the two children are of different genders, we need to consider the possible combinations of genders for the second and third children.
Here are the four possible combinations for the gender of the second and third children:
1. Boy, Boy
2. Boy, Girl
3. Girl, Boy
4. Girl, Girl
Since we know that the first child was a girl, we can eliminate the first combination (Boy, Boy). This leaves us with three remaining possibilities: Boy, Girl, Girl.
Out of these three possibilities, only one includes children of different genders (Boy, Girl). Therefore, the probability that the two children are of different genders is 1 out of 3, which can be expressed as 1/3 or 0.33 (rounded to two decimal places).
To calculate the probability that the two children are of different genders, we need to consider the possible outcomes.
Let's denote 'B' for a boy and 'G' for a girl.
Given that the first child is a girl, we have three possible scenarios for the second child: BG, GG, GB. Out of these three scenarios, only one has different genders, which is GB.
Therefore, the probability is 1 out of 3, or 1/3, that the two children are of different genders.