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56 problems match “probability”. Clear

Outlier percentage in a normal distribution ●●○○○ 20 ptsIn a normal distribution, a value is an outlier if it lies more than $1.5$ interquartile ranges above the upper quartile or more than $1.5$ interquartile ranges below the lower quartile. Using $z=\pm 0.67$ for the quartiles, what percent of values are outliers under this definition? Give the percent rounded to two decimal places.
Aces of spades and clubs adjacent ●●○○○ 20 ptsA standard 52-card deck is shuffled uniformly at random. Find the probability that the ace of spades and the ace of clubs are next to each other in the deck, in either order. Round to four decimal places.
Linear function avoiding the second quadrant ●●○○○ 20 ptsTwo different numbers are chosen from $-2,-1,1,2,3$ , the first as $k$ and the second as $b$ , to form the linear function $y=kx+b$ . Find the probability that the resulting line does not pass through the second quadrant. Give your answer as a decimal.
First, fifteenth or last ball red ●●○○○ 20 ptsA box contains 100 balls, of which 40 are red. The balls are drawn from the box one at a time at random, without replacement. Determine: 1. the probability that the first ball drawn is red, 2. the probability that the fifteenth ball drawn is red, 3. the probability that the last ball drawn is red. Give each answer as a decimal.
Second and third rolls exceed first ●●○○○ 20 ptsA fair six-sided die is rolled three times. Find the probability that the second and third rolls are both larger than the first roll. Round to two decimal places.
Birthday on a given day ●●○○○ 20 ptsA class has 30 students, and each student's birthday is equally likely to be any of 365 days. Find the probability that at least one student has a birthday on 5 November. Round to three decimal places.
Expected subscription rate after a letter ●●○○○ 20 ptsA magazine mailing list contains people who already subscribe and people who do not. 60% of current subscribers will subscribe again, and 25% of non-subscribers will now subscribe. In the last letter, 40% of those receiving it ordered a subscription. What percent of those receiving the current letter can be expected to order a subscription?
Prime sum of white and red balls ●●○○○ 20 ptsA bag contains 6 red balls and 8 white balls. Five balls are taken at random and placed in box $A$ , and the remaining 9 balls are placed in box $B$ . Find the probability that the sum of the number of white balls in box $A$ and the number of red balls in box $B$ is not a prime number. Round to four decimal places.
Probability of A from two unions ●●○○○ 20 ptsGiven $P(A \cup B)=0.7$ and $P(A \cup B')=0.9$ , determine $P(A)$ .
Birthday match among three people ●●○○○ 20 ptsThree people are in a room. Assuming each birthday is equally likely among 365 days (ignore leap years), find the probability that at least two of them share the same birthday. Round your answer to 9 decimal places.