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56 problems match “probability”. Clear

Rebid probability for close bids ●●●○○ 50 ptsTwo construction companies make bids $X$ and $Y$ on a remodeling project. The joint density of $X$ and $Y$ is uniform on the rectangle $2<x<2.5$ , $2<y<2.3$ . If $X$ and $Y$ are within 0.1 of each other, the companies are asked to rebid; otherwise the lower bidder gets the contract. Find the probability that the companies are asked to rebid. Round to two decimal places.
Male weight exceeds twice female weight ●●●○○ 50 ptsThe weights $X$ kg of male birds are normally distributed with mean $4.8$ and standard deviation $0.2$ . The weights $Y$ kg of female birds are normally distributed with mean $2.7$ and standard deviation $0.15$ . $X$ and $Y$ are independent. Find the probability that the weight of a randomly chosen male bird is more than twice the weight of a randomly chosen female bird. Give your answer correct to four decimal places.
Martian species height difference probability ●●●○○ 50 ptsSpecies 1 heights are normally distributed with mean 32 and variance 60. Species 2 heights are normally distributed with mean 22 and variance 70. A sample of 10 members of Species 1 and a sample of 14 members of Species 2 are drawn independently. Find the probability that the sample mean of Species 1 exceeds the sample mean of Species 2 by 5 or more. Round to three decimal places.
Expected people until first birthday match ●●●●○ 100 ptsAssume birthdays are independent and uniformly distributed over 365 days. People are questioned one at a time. Find the expected number of people questioned until the first person shares a birthday with someone already questioned (this person is counted). Round to two decimal places.
Minimum people covering every birthday ●●●●○ 100 ptsAssume a year has 365 equally likely birthdays, each person's birthday is independent of the others, and leap years are ignored. What is the minimum number of people needed so that the probability that every one of the 365 days is someone's birthday is greater than $0.5$ ?
Birthdays that are equal or adjacent ●●●●○ 100 ptsAssume 23 people have independent birthdays, each equally likely to be any of 365 days (February 29 is not considered), and January 1 and December 31 are considered adjacent. Find the probability that at least two people share the same birthday or have adjacent birthdays. Round to seven decimal places.