# If a couple is planning on having three children, what is the probability that only one will be...

## Question:

If a couple is planning on having three children, what is the probability that only one will be male?

## Probability and Mutually Exclusive Events

When we determine probability, we find how likely it is that certain events will occur. Sometimes these events are mutually exclusive. This means that they cannot occur at the same time. When we have mutually exclusive events, we can use this addition rule of probability {eq}P(A or B) = P(A) + P(B) {/eq} to find the probability that event A or event B will happen.

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Probability that only one of the three children will be male = 3/8.

One way to answer this question is to write down the ways that the births of the three children can occur.

 MMM MMF MFM FMM FFF FFM FMF MFF

We can see that out of the 8 possible outcomes, there are 3 outcomes that show just one male.

Probability = number of ways an event can occur / total number of outcomes

{eq}P = 3/8. {/eq}

Another way to think about this is to say that you are only interested in the times when one male is born. This can happen in the following three scenarios:

The male is born first (MFF), the male is born second (FMF), or the male is born third (FFM).

Each of these scenarios is mutually exclusive, and we are interested in the occurrence of the first, the second, or the third scenario.

{eq}P(A or B) = P(A) + P(B) = MFF + FMF + FFM = (1/8) + (1/8) + (1/8) = 3/8. {/eq}

(Unfortunately, the probability that all three kids will get along is more difficult to determine.) 