Prepare for Probability Interview with iQwizz | Difficulty Level: Intermediate | Rating: 4.5

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Question 1

The heights of adult males in a certain population are normally distributed with a mean of 175 cm and a standard deviation of 7 cm. What percentage of men are taller than 189 cm?

2.5%
5%
16%
32%

Question 2

A study shows that 60% of people who buy product A also buy product B. Is it necessarily true that 60% of people who buy product B also buy product A?

No, because the probabilities are independent of each other.
Yes, because buying product B makes it more likely someone buys product A.
Yes, because the probabilities must be equal.
No, because this only describes a conditional probability, not the reverse.

Question 3

A company's daily stock price fluctuations are approximately normally distributed with a mean of $0 (no change) and a standard deviation of $2. What is the probability that the stock price will increase by more than $4 on a given day?

0.9772
0.8413
0.1587
0.0228

Question 4

The time until a radioactive particle decays is modeled by an exponential distribution. If the average decay time is 10 seconds, what is the median decay time?

10 seconds
14.43 seconds
6.93 seconds
5 seconds

Question 5

You are simulating a random process with a known theoretical mean. After many simulations, you find that the average of your simulated results is significantly different from the expected theoretical mean. What is the MOST likely explanation for this discrepancy?

The theoretical mean is incorrect.
You have not run enough simulations for the Law of Large Numbers to take effect.
There is an error in your simulation code or methodology.
The Law of Large Numbers does not apply to simulations.

Question 6

A bag contains 5 red balls and 3 blue balls. Two balls are drawn randomly without replacement. What is the probability that the second ball drawn is red, given that the first ball drawn was blue?

Question 7

In a certain city, 40% of the people have brown hair, 30% have blonde hair, and 30% have black hair. Of the people with brown hair, 25% have blue eyes. If a person is selected at random, what is the probability the person has brown hair and blue eyes?

0.12
0.75
0.33
0.10

Question 8

In a normal distribution, what percentage of data falls within three standard deviations of the mean?

99.73%
68.27%
100%
95.45%

Question 9

A rare disease affects 1 in 10,000 people. A test for the disease is 99% accurate, meaning it correctly identifies 99% of people with the disease and 99% of people without the disease. If a person tests positive for the disease, what is the probability that they actually have it?

Question 10

Events A and B are independent. The probability of A occurring is 0.4, and the probability of B occurring is 0.6. What is the probability that at least one of the events, A or B, will occur?

1.00
0.50
0.24
0.76

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Question 1

The heights of adult males in a certain population are normally distributed with a mean of 175 cm and a standard deviation of 7 cm. What percentage of men are taller than 189 cm?

2.5%
5%
16%
32%

Question 2

A study shows that 60% of people who buy product A also buy product B. Is it necessarily true that 60% of people who buy product B also buy product A?

No, because the probabilities are independent of each other.
Yes, because buying product B makes it more likely someone buys product A.
Yes, because the probabilities must be equal.
No, because this only describes a conditional probability, not the reverse.

Question 3

0.9772
0.8413
0.1587
0.0228

Question 4

The time until a radioactive particle decays is modeled by an exponential distribution. If the average decay time is 10 seconds, what is the median decay time?

10 seconds
14.43 seconds
6.93 seconds
5 seconds

Question 5

The theoretical mean is incorrect.
You have not run enough simulations for the Law of Large Numbers to take effect.
There is an error in your simulation code or methodology.
The Law of Large Numbers does not apply to simulations.

Question 6

A bag contains 5 red balls and 3 blue balls. Two balls are drawn randomly without replacement. What is the probability that the second ball drawn is red, given that the first ball drawn was blue?

Question 7

0.12
0.75
0.33
0.10

Question 8

In a normal distribution, what percentage of data falls within three standard deviations of the mean?

99.73%
68.27%
100%
95.45%

Question 9

Question 10

Events A and B are independent. The probability of A occurring is 0.4, and the probability of B occurring is 0.6. What is the probability that at least one of the events, A or B, will occur?

1.00
0.50
0.24
0.76

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