Probability and Chance: Master the Fundamentals of Predicting Outcomes

Question 1

A bag contains 5 red, 3 blue, and 2 green balls. If a ball is selected randomly, what is the probability of drawing a red ball?

Accepted Answer

2/5

Answer

1/10

Answer

1/2

Answer

3/5

Question 2

A survey found that 60% of people prefer tea, while 40% prefer coffee. If 100 people are randomly selected, how many people would you expect to prefer coffee?

Accepted Answer

40

Answer

60

Answer

80

Answer

100

Question 3

A fair six-sided die is rolled. What is the probability of rolling an even number?

Accepted Answer

1/2

Answer

1/3

Answer

2/3

Answer

1/6

Question 4

A bag contains 5 red, 3 blue, and 2 green balls. If a ball is drawn at random and not replaced, what is the probability of drawing a blue ball on the second draw?

Accepted Answer

3/8

Answer

1/2

Answer

1/4

Answer

1/8

Question 5

When rolling a standard six-sided die, what is the likelihood of obtaining a 6?

Accepted Answer

1/6

Answer

1/2

Answer

1/3

Answer

1/4

Question 6

A bag contains 5 red and 3 blue balls. What is the probability of selecting a red ball?

Accepted Answer

5/8

Answer

1/2

Answer

2/3

Answer

3/5

Question 7

The probability of rain tomorrow is 30%. What is the likelihood of no rain?

Accepted Answer

70%

Answer

60%

Answer

50%

Answer

40%

Question 8

What is the likelihood of getting at least one head when flipping a coin twice?

Accepted Answer

3/4

Answer

1/2

Answer

1/4

Answer

1

Question 9

From a standard deck of 52 cards, what is the probability of drawing two aces without replacing the first ace?

Accepted Answer

1/2704

Answer

1/221

Answer

1/1326

Answer

1/17576

Question 10

A fair six-sided die is rolled. What is the probability of rolling a number greater than or equal to 4?

Accepted Answer

1/2

Answer

1/3

Answer

1/4

Answer

1/6

Question 11

A bag contains 10 balls numbered 1 to 10. If two balls are drawn at random without replacement, what is the probability of drawing a ball with an even number or a ball with a number greater than 6?

Accepted Answer

2/5

Answer

1/2

Answer

3/10

Answer

1/5

Question 12

A fair coin is tossed three times. What is the probability of getting exactly two heads?

Accepted Answer

3/8

Answer

1/8

Answer

1/2

Question 13

If the probability of an event occurring is 0.6, what is the probability of the event not occurring?

Accepted Answer

0.4

Answer

0.6

Answer

1

Question 14

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

Accepted Answer

2/15

Answer

1/6

Answer

8/15

Answer

4/15

Question 15

Events A and B are independent. If P(A) = 0.3 and P(B) = 0.5, what is P(A and B)?

Accepted Answer

0.15

Answer

0.8

Answer

0.5

Answer

0.2

Question 16

A student has a 70% chance of passing a math test and an 80% chance of passing a physics test. What is the probability of the student passing at least one of the tests?

Accepted Answer

0.94

Answer

0.56

Answer

0.06

Answer

0.14

Question 17

The probability of a machine producing a defective part is 0.02. What is the probability that out of 5 parts produced, exactly one is defective?

Accepted Answer

0.092

Answer

0.10

Answer

0.0032

Question 18

A bag contains 5 red balls and 3 blue balls. If two balls are drawn at random without replacement, what is the probability that both balls are red?

Accepted Answer

5/14

Answer

5/7

Answer

5/8

Answer

1/2

Question 19

A factory produces 1000 units per day, with a 5% defect rate. If a random sample of 50 units is selected, what is the probability that exactly 3 units are defective?

Accepted Answer

0.04046

Answer

0.15

Answer

0.05

Answer

0.25

Question 20

A company produces two types of engines, A and B. 70% of the engines produced are type A, and 30% are type B. Type A engines have a 2% defect rate, while type B engines have a 5% defect rate. If a randomly selected engine is found to be defective, what is the probability that it is type A?

Accepted Answer

0.28

Answer

0.02

Answer

0.7

Answer

0.35

Question 21

A survey found that 60% of engineers prefer brand A software, while 40% prefer brand B. If 10 engineers are randomly selected, what is the probability that exactly 6 of them prefer brand A?

Accepted Answer

0.2508

Answer

0.6

Answer

0.4

Answer

0.12

Question 22

A company is testing a new prototype. The probability of success on each trial is 0.8. What is the expected number of trials needed to achieve 3 successful trials?

Accepted Answer

3.75

Answer

3

Answer

4

Question 23

Two dice are rolled. What is the probability of getting a sum of 7?

Accepted Answer

1/6

Answer

1/4

Answer

1/3

Answer

1/12

Question 24

A box contains 10 resistors, 3 of which are defective. If 2 resistors are selected at random, what is the probability that at least one is defective?

Accepted Answer

17/30

Answer

3/10

Answer

1/3

Answer

7/30

Question 25

A machine has a 95% reliability rate. What is the probability that it will fail in 5 consecutive operations?

Accepted Answer

0.00003

Answer

0.25

Answer

0.95

Answer

0.05