Births in Vietnam In Vietnam, the probability of a baby being ...

Question

Births in Vietnam In Vietnam, the probability of a baby being a boy is 0.526 (based on the data available at this writing). For a family having four children, find the following.

d. The probability that at least one of the children is a girl.

Accepted Answer

Welcome back, everyone. In a manufacturing process, the probability that an item is defective is 0.474. For a quality inspection involving four items, calculate the following the probability that at least one of the items is defective. A says 0.148, B 0.776, C 0.923, and D 0.865. For this problem, we want to identify the probability that at least 1 of the items is defective when we are choosing a total of 4 items, right? So let's suppose that the variable X represents the number of defective items. We want to identify the probability that the random variable X is greater than or equal to 1, right? At least one of the items is defective. And what we can do is simply use the complement rule. So this probability is simply the difference between 1 and the probability that there are no defective items. So 1 minus P X equals 0. So what we want to do is simply identify the probability that there are no defective items, and we're going to perform this using the multiplication rule for independent events because our selections are independent. So we take 1, and then we have to subtract the probability that all 4 items are not defective. First of all, we're given the probability of a defective item 0.474, so its complement 1 minus 0.474 represents the probability of a non-effective item in a single trial, right? So that'd be 1 minus. 0.474, and we wish to have 4 non-defective items, so we have to raise it to the power of 4 using the multiplication rule, right? Non-defective, followed by non-defective, another 1, and the fourth one. So then we are subtracting 1 minusport C 1 minus 0.474 raises the power of 4. Which gives us the final probability of 0.923, and it corresponds to the answer choice C. Thank you for watching.

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Births in Vietnam In Vietnam, the probability of a baby being a boy is 0.526 (based on the data available at this writing). For a family having four children, find the following.

d. The probability that at least one of the children is a girl.

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Births in Vietnam In Vietnam, the probability of a baby being a boy is 0.526 (based on the data available at this writing). For a family having four children, find the following.d. The probability that at least one of the children is a girl.

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Births in Vietnam In Vietnam, the probability of a baby being a boy is 0.526 (based on the data available at this writing). For a family having four children, find the following.

d. The probability that at least one of the children is a girl.