200+ Probability-and-statistics Questions

Probability-and-statistics Questions Set 4:

Quiz Mode

If X is a random variable and a is a constant, then E(aX) is:

E(X)

a·E(X)

(a^2)·E(X)

Solution:

For two events A and B, if P(B') = 0.5 and P(A ∪ B) = 0.5, then P(A'|B') = ?

1.5

2.5

Solution:

Given that r=0.64, Σxy=75, σy=4, Σx²=144, find the number of observations taken.

Solution:

The relationship between standard deviation (SD) and quartile deviation (QD) is given by:

QD = 2/3(SD)

QD = 3/2(SD)

SD = 2/3(QD)

SD = 3/2(QD)

Solution:

If A and B are not independent events, then the probability of their intersection, P(A ∩ B), is

P(A) × P(A|B)

P(B) × P(A|B)

P(B) × P(B|A)

P(A) × P(B)

Solution:

In a binomial distribution, if p is the probability of success, q is the probability of failure, and n is the number of trials, what is the value of the mean?

npq

n/pq

n/p

Solution:

In a village, 25 babies were born in the last 50 days. Assuming the number of babies follows a Poisson distribution, find the probability that at least 1 baby is born per day.

0.6065

0.3935

0.9097

0.8286

Solution:

The probability that an e-commerce website delivers a damaged item is 5/32. If they deliver 80 items to customers on a day, what is the probability that exactly 20 of the delivered items are damaged?

0.0098

0.05

0.156

0.0064

Solution:

There are 2 containers, one containing 4 green and 3 red balls, and the other containing 3 green and 4 blue balls. If one ball is drawn at random from each container, what is the probability that one ball is red and the other is blue?

12/49

9/49

3/7

4/7

Solution:

An electronics company manufactures microchips, of which 3% are defective. The company sold 100 microchips to a distributor. Using the Poisson approximation, find the probability that none of the microchips sold will be defective.

0.15

1.0305

0.9704

0.0498

Probability-and-statistics Questions Set 4:

If X is a random variable and a is a constant, then E(aX) is:

Solution:

For two events A and B, if P(B') = 0.5 and P(A ∪ B) = 0.5, then P(A'|B') = ?

Solution:

Given that r=0.64, Σxy=75, σy=4, Σx²=144, find the number of observations taken.

Solution:

The relationship between standard deviation (SD) and quartile deviation (QD) is given by:

Solution:

If A and B are not independent events, then the probability of their intersection, P(A ∩ B), is

Solution:

In a binomial distribution, if p is the probability of success, q is the probability of failure, and n is the number of trials, what is the value of the mean?

Solution:

In a village, 25 babies were born in the last 50 days. Assuming the number of babies follows a Poisson distribution, find the probability that at least 1 baby is born per day.

Solution:

The probability that an e-commerce website delivers a damaged item is 5/32. If they deliver 80 items to customers on a day, what is the probability that exactly 20 of the delivered items are damaged?

Solution:

There are 2 containers, one containing 4 green and 3 red balls, and the other containing 3 green and 4 blue balls. If one ball is drawn at random from each container, what is the probability that one ball is red and the other is blue?

Solution:

An electronics company manufactures microchips, of which 3% are defective. The company sold 100 microchips to a distributor. Using the Poisson approximation, find the probability that none of the microchips sold will be defective.

Solution:

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