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

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Question 1

Suppose 30% of people in a city own a car and 20% own a bicycle. If car ownership and bicycle ownership are independent, what is the probability that a randomly selected person owns both a car and a bicycle?

50%
6%
10%
Cannot be determined

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?

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

Question 3

In a normal distribution, what percentage of the data falls within 2 standard deviations of the mean, excluding the data beyond 2 standard deviations?

68.27%
95.45%
99.73%
90.90%

Question 4

In a large dataset of customer purchase amounts, the average purchase is $50 with a standard deviation of $20. If we take 100 random samples of size 25 from this dataset, what will be the standard deviation of the distribution of these sample means?

Question 5

A bag contains 5 red marbles and 5 blue marbles. You draw two marbles from the bag without replacement. What is the probability that both marbles are red?

Question 6

A box contains 4 red balls and 6 green balls. Two balls are drawn consecutively without replacement. What is the probability that both balls are red?

8/15
1/6
4/25
2/15

Question 7

A company manufactures a product in two factories. Factory A produces 60% of the total output, and Factory B produces 40%. The defect rate at Factory A is 2%, and the defect rate at Factory B is 3%. If a randomly selected product is defective, what is the probability it came from Factory A?

Question 8

Events A and B are independent. The probability of event A is 0.3. The probability of event B is 0.6. What is the probability of both A and B occurring?

0.50
Cannot be determined from the given information.
0.90
0.18

Question 9

The time between arrivals of customers at a store is exponentially distributed with a mean of 5 minutes. What is the probability that the next customer will arrive in less than 2 minutes?

0.3297
0.4721
0.5279
0.6703

Question 10

A fair coin is tossed 1000 times. According to the Law of Large Numbers, which of the following statements is MOST likely to be true?

The number of heads will be exactly 500.
The proportion of heads will be exactly 0.5.
The proportion of heads will be closer to 0.5 than if the coin were tossed only 10 times.
The first 500 tosses will have more tails than heads.

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Question 1

50%
6%
10%
Cannot be determined

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?

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

Question 3

In a normal distribution, what percentage of the data falls within 2 standard deviations of the mean, excluding the data beyond 2 standard deviations?

68.27%
95.45%
99.73%
90.90%

Question 4

Question 5

A bag contains 5 red marbles and 5 blue marbles. You draw two marbles from the bag without replacement. What is the probability that both marbles are red?

Question 6

A box contains 4 red balls and 6 green balls. Two balls are drawn consecutively without replacement. What is the probability that both balls are red?

8/15
1/6
4/25
2/15

Question 7

Question 8

Events A and B are independent. The probability of event A is 0.3. The probability of event B is 0.6. What is the probability of both A and B occurring?

0.50
Cannot be determined from the given information.
0.90
0.18

Question 9

The time between arrivals of customers at a store is exponentially distributed with a mean of 5 minutes. What is the probability that the next customer will arrive in less than 2 minutes?

0.3297
0.4721
0.5279
0.6703

Question 10

A fair coin is tossed 1000 times. According to the Law of Large Numbers, which of the following statements is MOST likely to be true?

The number of heads will be exactly 500.
The proportion of heads will be exactly 0.5.
The proportion of heads will be closer to 0.5 than if the coin were tossed only 10 times.
The first 500 tosses will have more tails than heads.

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