A newly married couple expected a boy and a girl or four children, occuring boy or girl has equal probability. Find the probability of success of their expectations.
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To find the probability of success in this situation, we need to determine the probability of having at least one boy and one girl when having four children.
There are two possible successful outcomes:
1) Two boys and two girls (BBGG)
2) One boy and three girls (BGGG) or Three boys and one girl (GBBB)
To calculate the probability of each outcome, we need to consider that each child's gender is independent and equally likely to be a boy or a girl.
Probability of two boys and two girls (BBGG):
1/2 (probability of the first child being a boy) * 1/2 (probability of the second child being a boy) * 1/2 (probability of the third child being a girl) * 1/2 (probability of the fourth child being a girl) = 1/16
Probability of one boy and three girls (BGGG):
1/2 (probability of the first child being a boy) * 1/2 (probability of the second child being a girl) * 1/2 (probability of the third child being a girl) * 1/2 (probability of the fourth child being a girl) = 1/16
Probability of three boys and one girl (GBBB):
1/2 (probability of the first child being a girl) * 1/2 (probability of the second child being a boy) * 1/2 (probability of the third child being a boy) * 1/2 (probability of the fourth child being a boy) = 1/16
Therefore, the probability of success in having at least one boy and one girl when having four children is:
(1/16 + 1/16 + 1/16) = 3/16 or approximately 0.1875 (18.75%).