Grade 9 : Mathematics - 15. Probability (Set 3)

Question 1

Two coins are tossed simultaneously 200 times. The frequencies of various outcomes are recorded as follows: 2 Heads = 58 times, 1 Head = 84 times, 0 Heads = 58 times.

Find the empirical probability of getting at most 1 head.

Accepted Answer

C) 0.71

Answer

A) 0.29

Answer

B) 0.42

Answer

D) 0.58

Question 2

Outcome	1	2	3	4	5	6
Frequency	45	55	40	60	50	50

A die is thrown 300 times with outcomes recorded above. What is the empirical probability of getting a prime number outcome?

Accepted Answer

B) $\frac{29}{60}$

Answer

A) $\frac{11}{60}$

Answer

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

Answer

D) $\frac{31}{60}$

Question 3

A single card is drawn at random from a standard well-shuffled deck of 52 playing cards.

What is the probability that the card drawn is a red face card?

Accepted Answer

A) $\frac{3}{26}$

Answer

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

Answer

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

Answer

D) $\frac{6}{13}$

Question 4

A bag contains 12 red marbles, 15 blue marbles, 8 green marbles, and 15 yellow marbles.

One marble is drawn at random. What is the probability that the marble drawn is neither green nor red?

Accepted Answer

C) 0.60

Answer

A) 0.24

Answer

B) 0.40

Answer

D) 0.76

Question 5

A survey of 250 students was conducted to see if they prefer online learning or classroom learning. Results showed 160 students prefer classroom learning while 90 students prefer online learning.

What is the empirical probability that a randomly chosen student prefers online learning?

Accepted Answer

B) 0.36

Answer

A) 0.64

Answer

C) 0.45

Answer

D) 0.28

Question 6

A circular spinner is divided into 8 equal sectors numbered 1 through 8.

What is the probability that the pointer lands on a sector with a prime number?

Accepted Answer

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

Answer

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

Answer

C) $\frac{5}{8}$

Answer

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

Question 7

Cards numbered 11 to 60 are placed in a box and mixed thoroughly. One card is drawn at random.

What is the probability that the number on the drawn card is a multiple of 5?

Accepted Answer

A) $\frac{1}{5}$

Answer

B) $\frac{9}{50}$

Answer

C) $\frac{11}{50}$

Answer

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

Question 8

Two fair dice are rolled simultaneously.

What is the probability that the sum of the numbers appearing on the top faces is a perfect square?

Accepted Answer

C) $\frac{7}{36}$

Answer

A) $\frac{5}{36}$

Answer

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

Answer

D) $\frac{2}{9}$

Question 9

A basketball player attempts 80 free throws during a season and succeeds in 64 of them.

What is the empirical probability that on her next free throw attempt, she misses?

Accepted Answer

B) 0.20

Answer

A) 0.80

Answer

C) 0.16

Answer

D) 0.25

Question 10

Weather records over 200 consecutive days show that the daily weather forecast was accurate on 144 days.

What is the probability that on a randomly chosen day from this period, the forecast was NOT accurate?

Accepted Answer

B) 0.28

Answer

A) 0.72

Answer

C) 0.32

Answer

D) 0.22

Question 11

A manufacturing plant produces 800 components in a batch. Quality control inspection finds 32 defective components.

What is the probability that a component selected at random from the batch is non-defective?

Accepted Answer

C) 0.96

Answer

A) 0.04

Answer

B) 0.92

Answer

D) 0.88

Question 12

Outcome	1	2	3	4	5	6
Frequency	45	55	40	60	50	50

The blood groups of 50 students are recorded above. A student is selected at random. What is the probability that the student has neither blood group A nor group O?

Accepted Answer

A) 0.36

Answer

B) 0.64

Answer

C) 0.24

Answer

D) 0.12

Question 13

Consider the letters in the word "MATHEMATICS".

If one letter is chosen at random, what is the probability that it is a vowel?

Accepted Answer

B) $\frac{4}{11}$

Answer

A) $\frac{3}{11}$

Answer

C) $\frac{5}{11}$

Answer

D) $\frac{7}{11}$

Question 14

A coin is tossed 150 times. Heads appeared 78 times and Tails appeared 72 times.

What is the empirical probability of getting a Tail on a random toss?

Accepted Answer

B) 0.48

Answer

A) 0.52

Answer

C) 0.50

Answer

D) 0.42

Question 15

A container holds 9 red, 11 white, and 10 blue poker chips.

A chip is drawn at random. What is the probability that the chip is NOT white?

Accepted Answer

B) $\frac{19}{30}$

Answer

A) $\frac{11}{30}$

Answer

C) $\frac{7}{10}$

Answer

D) $\frac{13}{30}$

Question 16

Outcome	1	2	3	4	5	6
Frequency	45	55	40	60	50	50

The test scores of 60 students are grouped as above. What is the probability that a randomly chosen student scored more than 70 marks?

Accepted Answer

A) 0.30

Answer

B) 0.45

Answer

C) 0.25

Answer

D) 0.70

Question 17

A ticket is drawn at random from a box containing tickets numbered 1 through 25.

What is the probability that the number on the ticket is divisible by both 3 and 4?

Accepted Answer

B) $\frac{2}{25}$

Answer

A) $\frac{4}{25}$

Answer

C) $\frac{7}{25}$

Answer

D) $\frac{1}{5}$

Question 18

A fair coin is tossed and a standard 6-sided die is rolled simultaneously.

What is the probability of getting 'Heads' on the coin AND a prime number on the die?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 19

A jar contains red, blue, and green marbles in the ratio $3 : 4 : 5$.

A marble is drawn at random. What is the probability that the drawn marble is NOT green?

Accepted Answer

B) $\frac{7}{12}$

Answer

A) $\frac{5}{12}$

Answer

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

Answer

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

Question 20

Two coins are tossed 300 times simultaneously. The results show 2 Heads occurred 75 times, 1 Head occurred 150 times, and 0 Heads occurred 75 times.

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

Accepted Answer

C) 0.75

Answer

A) 0.25

Answer

B) 0.50

Answer

D) 0.80

Grade 9 : Mathematics - 15. Probability (Set 3)