Grade 9 : Mathematics - 15. Probability (Set 4)

Question 1

Number of Heads	3	2	1	0
Frequency	32	72	64	32

Three coins were tossed simultaneously 200 times, and the frequencies of outcomes were recorded as shown in the table above. What is the empirical probability of getting at most 1 head?

Accepted Answer

A) 0.48

Answer

B) 0.32

Answer

C) 0.52

Answer

D) 0.16

Question 2

Number of Heads	3	2	1	0
Frequency	32	72	64	32

A single die was rolled 150 times and the results were recorded in the table above. What is the empirical probability of getting a prime number?

Accepted Answer

B) $1/2$

Answer

A) $1/3$

Answer

C) $2/5$

Answer

D) $3/5$

Question 3

A box contains 12 red balls, 18 blue balls, and 20 green balls. A ball is drawn at random from the box.

What is the probability that the drawn ball is NOT red?

Accepted Answer

C) 0.76

Answer

A) 0.24

Answer

B) 0.36

Answer

D) 0.64

Question 4

A survey of 250 students was conducted to see whether they like or dislike algebra. The results showed that 135 students like algebra while 115 students dislike algebra.

If a student is chosen at random from this group, what is the empirical probability that the student dislikes algebra?

Accepted Answer

B) 0.46

Answer

A) 0.54

Answer

C) 0.35

Answer

D) 0.23

Question 5

Two coin tosses are repeated 300 times simultaneously. The results are: 2 Heads = 85 times, 1 Head = 130 times, 0 Heads = 85 times.

What is the empirical probability of getting at least 1 head?

Accepted Answer

B) $43/60$

Answer

A) $17/60$

Answer

C) $13/30$

Answer

D) $7/12$

Question 6

A box contains 30 identical cards numbered from 1 to 30. One card is drawn at random from the box.

What is the probability that the number on the drawn card is a multiple of 4 or 6?

Accepted Answer

A) $1/3$

Answer

B) $2/5$

Answer

C) $7/30$

Answer

D) $11/30$

Question 7

If the probability of an event $E$ occurring is $P(E) = 0.08$, what is the probability of the complement event $P( ext{not } E)$?

Accepted Answer

C) 0.92

Answer

A) 0.02

Answer

B) 0.82

Answer

D) 0.98

Question 8

Number of Heads	3	2	1	0
Frequency	32	72	64	32

A spinner with five colored regions was spun 250 times. The resulting frequencies are listed in the table above. What is the empirical probability that the spinner lands on either Blue or Green?

Accepted Answer

A) 0.46

Answer

B) 0.26

Answer

C) 0.38

Answer

D) 0.52

Question 9

A coin is tossed 100 times. If heads appear 45 times and tails appear 55 times, what is the empirical probability of getting a tail?

Accepted Answer

B) 0.55

Answer

A) 0.45

Answer

C) 0.50

Answer

D) 0.10

Question 10

A standard six-sided die is rolled once. What is the theoretical probability of getting a prime number?

Accepted Answer

C) $\frac{1}{2}$

Answer

A) $\frac{1}{6}$

Answer

B) $\frac{1}{3}$

Answer

D) $\frac{2}{3}$

Question 11

A bag contains 5 red balls, 8 white balls, and 4 green balls. If one ball is drawn at random, what is the probability that the ball drawn is NOT red?

Accepted Answer

C) $\frac{12}{17}$

Answer

A) $\frac{5}{17}$

Answer

B) $\frac{8}{17}$

Answer

D) $\frac{13}{17}$

Question 12

Two coins are tossed simultaneously 500 times. Two heads are obtained 105 times, one head 275 times, and no head 120 times. What is the empirical probability of getting at least one head?

Accepted Answer

C) 0.76

Answer

A) 0.21

Answer

B) 0.55

Answer

D) 0.24

Question 13

A card is drawn at random from a well-shuffled deck of 52 playing cards. What is the probability that the card drawn is a face card?

Accepted Answer

B) $\frac{3}{13}$

Answer

A) $\frac{1}{13}$

Answer

C) $\frac{4}{13}$

Answer

D) $\frac{12}{13}$

Question 14

What is the probability that an ordinary (non-leap) year chosen at random contains 53 Sundays?

Accepted Answer

A) $\frac{1}{7}$

Answer

B) $\frac{2}{7}$

Answer

C) $\frac{52}{365}$

Answer

D) $\frac{53}{365}$

Question 15

In a survey of 200 students, 135 like statistics while 65 do not like it. What is the probability that a student chosen at random does NOT like statistics?

Accepted Answer

B) 0.325

Answer

A) 0.675

Answer

C) 0.135

Answer

D) 0.200

Question 16

If the probability of an event $E$ occurring is $P(E) = 0.08$, what is the probability of the event 'not $E$'?

Accepted Answer

C) 0.92

Answer

A) 0.02

Answer

B) 0.82

Answer

D) 0.98

Question 17

A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random, what is the probability that it bears a two-digit number?

Accepted Answer

B) $\frac{9}{10}$

Answer

A) $\frac{1}{10}$

Answer

C) $\frac{8}{9}$

Answer

D) $\frac{81}{100}$

Question 18

A circular spinner is divided into 8 equal sectors numbered 1 through 8. What is the probability that the spinner lands on a sector that is a multiple of 3?

Accepted Answer

B) $\frac{1}{4}$

Answer

A) $\frac{1}{8}$

Answer

C) $\frac{3}{8}$

Answer

D) $\frac{1}{2}$

Question 19

A bag contains 6 red marbles, 4 blue marbles, and $x$ yellow marbles. If the probability of randomly drawing a yellow marble is $\frac{1}{3}$, what is the value of $x$?

Accepted Answer

C) 5

Answer

A) 3

Answer

B) 4

Answer

D) 6

Grade 9 : Mathematics - 15. Probability (Set 4)