In a family with two children, what are the probabilities of the following outcomes, assuming that the birth of boys and girls is equally likely? a. Both are boys.b. The first is a girl and the second a boy. c. Neither is a girl. d. At least one is a girl.

I am questioning myself because this seems too easy. The answer would be D, right?

If the chances are equally likely, then the outcome of two children would be one boy and one girl, correct?

I am supposed to figure out the probabilities of each statement...does anyone know how to do that?

In the question you are dealing with a 1/2 probability rate, so in

a-it wouls be 2 of the 1/2 rates which is 25%
b-it would be the same b/c its still two 1/2 senerios, so 25% again
c-same thing 25%
d-this is a 75% chance b/c the secod child is still an unknown factor and could be either a girl or boy

Thank you so much. I understood there was a 50% chance of a boy and a 50% chance of a girl, I just didn't know how to equate the probabilities.

Let's go through each outcome step by step and calculate the probabilities:

a. To calculate the probability of both children being boys, we need to consider that there are four equally likely outcomes: BB, BG, GB, and GG (where B represents a boy and G represents a girl). Out of these four outcomes, only one has both children as boys. Therefore, the probability of both children being boys is 1 out of 4, which can be simplified to 1/4.

b. To calculate the probability of the first child being a girl and the second child being a boy, we need to consider that there are four equally likely outcomes: BB, BG, GB, and GG. Out of these four outcomes, two have a girl as the first child and a boy as the second child (BG and GG). Therefore, the probability of the first child being a girl and the second child being a boy is 2 out of 4, which can be simplified to 2/4 or 1/2.

c. To calculate the probability of neither child being a girl, we need to consider that there are four equally likely outcomes: BB, BG, GB, and GG. Out of these four outcomes, only one has neither child being a girl (BB). Therefore, the probability of neither child being a girl is 1 out of 4, which can be simplified to 1/4.

d. To calculate the probability of at least one child being a girl, we need to consider that there are four equally likely outcomes: BB, BG, GB, and GG. Out of these four outcomes, three have at least one girl (BG, GB, and GG). Therefore, the probability of at least one child being a girl is 3 out of 4, which can be simplified to 3/4.

So, the correct answer for each outcome is:
a. The probability of both being boys is 1/4.
b. The probability of first child being a girl and second child being a boy is 1/2.
c. The probability of neither being a girl is 1/4.
d. The probability of at least one being a girl is 3/4.

Therefore, the answer is not just option D, but all four options have non-zero probabilities.