Births in the United States In the United States, the true pro...

Question

Births in the United States In the United States, the true probability of a baby being a boy is 0.512 (based on the data available at this writing). For a family having three children, find the following.

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

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

Accepted Answer

Welcome back, everyone. In a greenhouse, the probability that a seed will successfully germinate at 0.85. A gardener plants 3 seeds, each in a separate pot and under the same conditions. What is the probability that at least one of the seeds fails to germinate? A 0.1500. B 0.3859 C 0.6141, and D 0.8500. First of all, let's define an event A. Let's suppose that it represents an event that at least one of the seeds fails to germinate. So we're going to say at least. One Fails So essentially what we want to do in this problem is identify the probability of an event A, and we know that we're dealing with independent events, right? Because the probability of one seed successfully germinating doesn't affect the probability of another seed to germinate, right? We are also going to define the probability of a in terms of its complement using the properties of probabilities. E of A is equal to 1 minus the probability of a bar, right? The complement or the opposite event. Let's understand it a bar. Is the opposite event. If a means at least one fails, then a bar or basically the complement of a represents an event that all. 3 Terminate And this is going to be very helpful in solving the problem, because we can identify the probability of the complement of A. And it says that we're looking for the probability of all three seeds germinating. Now, because we have independent events, we can just say that the probability of a bar is going to be 0.85. In other words, the probability of the first seed germinating. Multiplied by 0.85 and multiplied by 0.85 again, right? So we're using the multiplication rule for independent events. And now what we can do is simply write it as 0.85 cubed and now substitute it back into our expression. P of A is going to be equal to 1 minus 0.85 cub. And this is equal to 0.3859, expressed to 4 decimal places, which corresponds to the answer choice B. Thank you for watching.

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