Out of 800 families with 5 children each how many would you expect to have a
5 girls, 3 boys and 2 girls, either 2 or 3 boys,atleast one boy? Assume equal probability for boys and girls.
To calculate the expected number of families with a particular combination of children, we need to determine the probability of each combination occurring.
There are three combinations to consider:
1. 5 girls
2. 3 boys and 2 girls
3. Either 2 or 3 boys
Let's calculate each probability:
1. 5 girls:
The probability of each child being a girl is 1/2, so the probability of having 5 girls in a family is (1/2)^5 = 1/32.
2. 3 boys and 2 girls:
The probability of having 3 boys and 2 girls is the combination of Boy-Boy-Boy-Girl-Girl and Girl-Girl-Boy-Boy-Boy. Both combinations have the same probability.
The probability of each child being a boy is 1/2 and the probability of each child being a girl is also 1/2.
Therefore, the probability of having 3 boys and 2 girls is 2 * (1/2)^5 = 2/32 = 1/16.
3. Either 2 or 3 boys:
The probability of having 2 boys and 3 girls is the combination of Boy-Boy-Girl-Girl-Girl, Boy-Girl-Boy-Girl-Girl, and Girl-Boy-Boy-Girl-Girl. All three combinations have the same probability.
The probability of each child being a boy is 1/2 and the probability of each child being a girl is also 1/2.
Therefore, the probability of having 2 boys and 3 girls is 3 * (1/2)^5 = 3/32.
To calculate the expected number of families for each combination, we multiply the probability by the total number of families:
1. Expected number of families with 5 girls = (1/32) * 800 = 25.
2. Expected number of families with 3 boys and 2 girls = (1/16) * 800 = 50.
3. Expected number of families with either 2 or 3 boys = (3/32) * 800 = 75.
In conclusion, we would expect to have 25 families with 5 girls, 50 families with 3 boys and 2 girls, and 75 families with either 2 or 3 boys.