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There are several reasons that the question cannot have a proper answer. The first is that children's gender are not independent events. It is, therefore, wrong to multiply probabilities. Second, the probability of a girl is not 1/2. Current statistics show that it is approx 0.48.
However, if you wish to ignore these relevant facts, the [incorrect] answer that is expected is 1/4.
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What is the probability that in a family of four children that all four children are girls?
The probably of four girls in a family with four children is 1/16. I got this answer because: Probability of a girl is 1/2 and to get all girls you would multiply it by 1/2 for the rest of the girls.
What is the probability that a family with 4 children has at least 2 girls?
Assuming that boys and girls are equally likely, it is 11/16.
What is the probability of having exactly 2 boys out of 6 children?
The answer depends on whether the children are picked at random. If they were selected from inside a girls' school the probability should be quite close to 0. Likewise, if the children were picked inside a boys' school. If six children are picked at random from a large group of children with an equal number of boys and girls, then the answer is 6C2*(1/2)6 = 15/32 = 0.47, approx.
Theoretical probability that a family of 4 children will be all girls?
4/6=2/4 n(s)=3 6
What is the probability that a family of four children has at least 2 girls?
Going by the assumption that the probability of a child being a girl is 1/2, and that the events are independent, then the probabilities of different numbers of girls are as follows: P(0 girls) = 1/2 ^ 4 = 1/16 P(1 girl) = 4 * (1/2) * (1/2 ^ 3) = 1/4 P(2 girls) = 6 * (1/2 ^ 2) * (1/2 ^ 2) = 3/8 P(3 girls) = 4 * (1/2 ^ 3) * (1/2) = 1/4 P(4 girls) = 1/2 ^ 4 = 1/16 Therefore the probability of at least 2 girls = 3/8 + 1/4 + 1/16 = 11/16
