A newlywed couple wishes to have 3 children. What is the probability of having exactly 2 boys?

prob(2boys of 3 children)

= C(3,2)(1/2)^2 (1/2)
= 3/8

or, you could list them:
BBB
BBG
BGB
BGG
GBB
GBG
GGB
GGG
There are 3 with 2 boys, 1 girl
prob(your event) = 3/8

Well, the probability of having a boy or a girl is like flipping a coin. So if the probability of having a boy is 1/2, and the probability of having a girl is also 1/2, then the probability of having exactly 2 boys out of 3 children is like flipping a coin three times and getting two heads.

Now, if I were to flip a coin three times and try to get two heads, I would probably end up flipping it into a tree or down a sewer grate, because my circus skills aren't the greatest. But in theory, the probability would be 3/8.

But remember, probabilities are just predictions, and life is full of surprises! So while the probability might be 3/8, in reality, you could end up with three boys, three girls, or even a family of clowns! Who knows? Life is a circus after all!

To calculate the probability of having exactly 2 boys, we need to determine the possible outcomes and then calculate the probability of each outcome.

In this scenario, the couple wishes to have 3 children, so there can be a total of 2^3 = 8 possible outcomes, as each child can either be a boy or a girl.

Let's list all the possible outcomes:
1. BBB (3 boys)
2. BBG (2 boys, 1 girl)
3. BGB (2 boys, 1 girl)
4. BGG (1 boy, 2 girls)
5. GBB (2 boys, 1 girl)
6. GBG (1 boy, 2 girls)
7. GGB (1 boy, 2 girls)
8. GGG (3 girls)

Out of these 8 possible outcomes, there are 3 outcomes that have exactly 2 boys: BBG, BGB, and GBB. The probability of each outcome is 1/8, as each outcome is equally likely.

Therefore, the probability of having exactly 2 boys is 3/8 or 0.375, which can also be expressed as 37.5%.

To determine the probability of having exactly 2 boys, we need to consider different possibilities for the gender of the three children.

There are three ways to arrange two boys and one girl: BBG, BGB, and GBB. We need to find the probability of each arrangement and then add them up.

The probability of having a boy or a girl is equal, as there is a 50% chance for each outcome. So, the probability of having a boy is 1/2, and the probability of having a girl is also 1/2.

Let's calculate the probability for each arrangement:

BBG: The probability of having a boy is 1/2, the probability of having another boy is also 1/2, and the probability of having a girl is 1/2. Therefore, the probability of BBG is (1/2) * (1/2) * (1/2) = 1/8.

BGB: Similarly, the probability of BGB is (1/2) * (1/2) * (1/2) = 1/8.

GBB: The probability of GBB is (1/2) * (1/2) * (1/2) = 1/8.

Now, we add up the probabilities of each arrangement to find the total probability of having exactly 2 boys:

1/8 + 1/8 + 1/8 = 3/8

Therefore, the probability of having exactly 2 boys out of 3 children is 3/8 or 37.5%.

Note: This calculation assumes that the gender of each child is independent of the others, with an equal chance of being a boy or a girl.