Applying Complementary Events In Problem Solving Quiz

1) What is the probability of not landing on Red in one spin?

3/8

5/8

1/2

1/8

Not Red = 1 − 3/8 = 5/8.

Explanation

Not Red = 1 − 3/8 = 5/8.

2) What is the probability of landing on Blue at least once in two spins?

1 − (6/8)

(1/4)²

1 − (1/4)²

1 − (3/4)²

At least one Blue = 1 − (no Blue)² = 1 − (3/4)².

Explanation

At least one Blue = 1 − (no Blue)² = 1 − (3/4)².

3) What is the probability that in three spins, the spinner never lands on Yellow?

(1/8)³

1 − (1/8)³

(7/8)³

1 − (7/8)³

Not Yellow each time = (7/8)³.

Explanation

Not Yellow each time = (7/8)³.

4) What is the probability of landing on Green or Blue at least once in two spins?

1 − (1/2)²

(1/2)²

1 − (1/2)³

(3/8)²

P(G or B) = 2/8 + 2/8 = 1/2 → at least once = 1 − (1 − 1/2)².

Explanation

P(G or B) = 2/8 + 2/8 = 1/2 → at least once = 1 − (1 − 1/2)².

5) In four spins, what is the probability of landing on Red at least once?

(3/8)⁴

(5/8)⁴

1 − (3/8)⁴

1 − (5/8)⁴

At least one Red = 1 − (no Red)⁴ = 1 − (5/8)⁴.

Explanation

At least one Red = 1 − (no Red)⁴ = 1 − (5/8)⁴.

6) What is the probability that in two spins, you do not land on Yellow or Green in either spin?

1 − (3/8)²

1 − (5/8)²

(5/8)²

(3/8)²

Not (Y or G) per spin = 1 − (1/8+2/8) = 5/8 → (5/8)².

Explanation

Not (Y or G) per spin = 1 − (1/8+2/8) = 5/8 → (5/8)².

7) A fair coin is flipped 5 times. What is the probability of getting at least one tail?

(1/2)⁵

1 − (1/2)⁵

1 − (1/2)⁴

(1/2)⁴

At least one tail = 1 − (all heads) = 1 − (1/2)⁵.

Explanation

At least one tail = 1 − (all heads) = 1 − (1/2)⁵.

8) In a class of 30 students, 18 play soccer. If a student is chosen at random, what is the probability they do not play soccer?

18/30

1 − 12/30

12/30

0.6

Not soccer = (30 − 18)/30 = 12/30.

Explanation

Not soccer = (30 − 18)/30 = 12/30.

9) A bag contains 5 red, 4 blue, and 1 yellow marble. One marble is drawn at random and replaced. What is the probability that in three draws you never pick a yellow marble?

(9/10)³

1 − (9/10)³

1 − (1/10)³

(1/10)³

Not yellow each draw = 9/10 → three draws = (9/10)³.

Explanation

Not yellow each draw = 9/10 → three draws = (9/10)³.

10) A password requires choosing a digit from 0–9. What is the probability that a randomly chosen digit is not a prime number? (Prime digits: 2, 3, 5, 7)

1/10

3/10

6/10

8/10

Non-prime digits = 10 − 4 = 6 → 6/10.

Explanation

Non-prime digits = 10 − 4 = 6 → 6/10.

11) A student guesses on a 4-question true/false quiz. What is the probability they get at least one question wrong?

(1/2)⁴

1 − (1/2)³

(1/2)³

1 − (1/2)⁴

At least one wrong = 1 − (all correct) = 1 − (1/2)⁴.

Explanation

At least one wrong = 1 − (all correct) = 1 − (1/2)⁴.

12) A die is rolled twice. What is the probability of not rolling a 6 on either roll?

1 − (1/6)²

(5/6)²

(1/6)²

1 − (5/6)²

Not 6 per roll = 5/6 → both rolls = (5/6)².

Explanation

Not 6 per roll = 5/6 → both rolls = (5/6)².

13) The probability that it rains on any given day is 0.3, independently day to day. What is the probability that it doesn’t rain at all over a 3-day weekend?

1 − 0.3³

0.7³

1 − 0.7³

0.3³

No rain for 3 days = (0.7)³.

Explanation

No rain for 3 days = (0.7)³.

14) A box has 12 bulbs, 3 defective and 9 good. One bulb is selected at random. What is the probability that it is not defective?

9/12

5/12

3/12

1/12

Not defective = 9/12.

Explanation

Not defective = 9/12.

15) A standard deck has 52 cards. What is the probability that a single card drawn is not a heart?

1/4

3/4

13/52

1 − 3/4

Hearts = 13/52 → not heart = 39/52 = 3/4.

Explanation

Hearts = 13/52 → not heart = 39/52 = 3/4.

16) A web server has a 2% chance of being down on any given minute, independently each minute. What is the probability that it is up for all 10 minutes of a check?

1 − 0.02¹⁰

1 − 0.98¹⁰

0.02¹⁰

0.98¹⁰

Up per minute = 0.98 → all 10 minutes = 0.98¹⁰.

Explanation

Up per minute = 0.98 → all 10 minutes = 0.98¹⁰.

17) A student will attempt a skill until they succeed. Each attempt has a 0.6 chance of success, independent of previous attempts. What is the probability they fail both of their first two attempts?

1 − 0.6²

1 − 0.4²

0.4²

0.6²

Fail per attempt = 0.4 → two fails = 0.4 × 0.4 = 0.4².

Explanation

Fail per attempt = 0.4 → two fails = 0.4 × 0.4 = 0.4².

18) A game wheel has equally likely outcomes labeled A, B, C, D, E. What is the probability of not landing on A in three independent spins?

(4/5)³

1 − (4/5)³

1 − (1/5)³

(1/5)³

Not A per spin = 4/5 → three spins = (4/5)³.

Explanation

Not A per spin = 4/5 → three spins = (4/5)³.

19) In a raffle, 200 tickets are sold and 5 are winners. If you buy one ticket, what is the probability that you do not win?

5/200

195/200

7/200

100/200

Not winning = 1 − 5/200 = 195/200.

Explanation

Not winning = 1 − 5/200 = 195/200.

20) A survey shows 40% of people prefer tea to coffee. If two people are chosen independently at random, what is the probability that at least one prefers coffee?

(0.6)²

0.4 × 0.6

1 − (0.6)²

1 − (0.4)²

Coffee = 0.6. At least one coffee = 1 − (both tea) = 1 − (0.4)².

Explanation

Coffee = 0.6. At least one coffee = 1 − (both tea) = 1 − (0.4)².