Assuming boys and girls are equally​ likely, find the probability of a couple having a baby boy when their fifth child is​ born, given that the first four children were all boys

In the United States, the true probability of a baby being a boy is 0.512 (based on the data available at this writing). Among the next six randomly selected births in the United States, what is the probability that at least one of them is a girl?

Based on a poll conducted through thee-edition of USA Today, 67% of Internet users are more careful about personal information when using a public Wi-Fi hotspot. What is the probabili ty that among four randomly selected Internet users, at least one is more careful about personal information when using a public Wi-Fi hotspot? How is the result affected by the additional information that the survey subjects volunteered to respond?

Find the probability of a couple having a baby girl when their sixth child is born, given that that the first five children were all girls. Assume boys and girls are equally likely. Is the result the same as the probability of getting all girls among six children.

Find the probability of a couple having a baby girl when their third child is born, given that the first two children were both girls. Is the result the same as the probability of getting three girls among three children?

Let A = the event of getting at least one defective iPhone when 3 iPhones are randomly selected with replacement from a batch. Write a statement describing event $\overline A$.

A couple intends to have four children. Assume that having a boy and having a girl are equally likely events. (a) List the sample space of this experiment. (b) Find the probability that the couple will have only boys. (c) Find the probability that the couple will have two boys and two girls. (d) Find the probability that the couple will have four children of the same gender (e) Find the probability that the couple will have at least two girls.

Find the probability that when a couple has four children, at least one of them is a girl. (Assume that boys and girls are equally likely.)

Assuming that boys and girls are equally likely, find the probability of getting all girls when 1000 babies are born. Does the result indicate that such an event is impossible?

When the author observed a sobriety checkpoint conducted by the Dutchess County Sheriff Department, he saw that 676 drivers were screened and 6 were arrested for dri vi ng while intoxicated. Based on those res ults, we can estimate that P(I) = 0.00888, where I denotes the event of screening a driver and getting someone who is intoxicated. What does P($\overline I$) denote, and what is its value?

Among 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware, which is software programmed into the device (based on data from "Pacemaker and ICD Generator Malfunctions," by Maisel et al. , Journal of the American Medical Association, Vol. 295 , No. 16). If the firmware is tested in three different pacemakers randomly selected from this batch of 8834 and th e enti re batch is accepted if there are no fa ilures, what is the probability that the firmware in the entire batch will be accepted? Is this procedure likely to result in the entire batch being accepted?

A couple has three children. Assuming independence and that the probability of a boy is

$$\dfrac{1}{2}$$

, determine the probability that at least one child is a girl.

Based on a poll conducted through the e-edition of USA Today, $67 \%$ of Internet users are more careful about personal information when using a public Wi-Fi hotspot. What is the probability that among four randomly selected Internet users, at least one is more careful about personal information when using a public Wi-Fi hotspot? How is the result affected by the additional information that the survey subjects volunteered to respond to?

Assume that different groups of couples use the XS ORT method of gender selection and each couple gives birth to one baby. The XSORT method is designed to increase the likelihood that a baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consist of 36 couples. Find the mean and standard deviation for the numbers of girls in groups of 36 births.