I feel as though I am missing something here...Suppose a family wants to have 3 children. Find the probability that the family has at least 1 boy. Help?
To find the probability that a family has at least 1 boy out of 3 children, we can use the concept of complement probability.
The complement probability of an event is the probability of the event not occurring. In this case, we can find the complement probability of having all girls (no boys) and then subtract it from 1 to find the probability of having at least 1 boy.
Step 1: Find the probability of having all girls (no boys)
To calculate the probability of having all girls, we need to consider each child's gender. Since each child can either be a boy or a girl, there are two possibilities for each child and thus 2^3 = 8 total possible outcomes for all 3 children.
Out of these 8 possibilities, only one possibility has all girls. Therefore, the probability of having all girls is 1/8.
Step 2: Find the complement probability
The complement probability of having all girls (no boys) is simply the probability of not having all girls, which is 1 - 1/8 = 7/8.
Step 3: Find the probability of having at least 1 boy
Since the complement probability of having all girls is the probability of having at least 1 boy, the probability of having at least 1 boy is 7/8.
Therefore, the probability that the family has at least 1 boy out of 3 children is 7/8 or approximately 0.875.