10th grade statistics and probability

Question 1

Survey: Likes science & is in Club — 25; Likes science & not in Club — 16; Doesn't like science & in Club — 6; neither — 19. Given a student is in the Club, what is the probability they like science? Simplest form.

Answer (as a fraction)

Question 2

P(A) = 0.5, P(B) = 0.5 and P(A and B) = 0.4. Find P(A or B).

Answer 

Question 3

In a class, P(plays sport) = 0.7, P(plays an instrument) = 0.3 and P(sport or instrument) = 0.9. Find P(sport and instrument).

Answer 

Question 4

P(A) = 0.2, P(B) = 0.4 and P(A and B) = 0.08. Are A and B independent?

• A. Yes
• B. No

Question 5

Set A: 16, 21, 24, 27, 32. Set B: 23, 24, 24, 25, 24. Which set has the larger standard deviation?

• A. A
• B. B
• C. They are equal

Question 6

A card is drawn from a standard 52-card deck. Find the probability that it is a number card from 2 to 10 or a diamond. Give a fraction in simplest form.

Answer (as a fraction)

Question 7

A playlist has 7 pop songs and 5 rock songs. Two different songs are picked at random. Find P(one of each type) as a fraction in simplest form.

Answer (as a fraction)

Question 8

Set X: 56, 57, 58, 59, 60 Set Y: 46, 52, 58, 64, 70 Both have mean 58. Which set has the larger standard deviation?

• A. X
• B. Y
• C. They are equal

Question 9

A bag has 8 red and 5 blue counters. Two are taken out without replacement. Find P(both red) as a fraction in simplest form.

Answer (as a fraction)

Question 10

Estimate the mean from this grouped table: 0–10: 5, 10–20: 5, 20–30: 6, 30–40: 5. Round to 1 decimal place.

Answer 

Question 11

Some lengths have standard deviation 10 cm. Every length is multiplied by 4. What is the new standard deviation, in cm?

Answer 

Question 12

A box has 2 vanilla and 3 chocolate biscuits. Two are eaten at random. Find P(at least one chocolate) as a fraction in simplest form.

Answer (as a fraction)

Question 13

Find the population standard deviation of: 3, 9

Answer 

Question 14

In a histogram, a bar covers a class of width 20 and has frequency density 0.5. What is the frequency?

Answer 

Question 15

Survey: Likes science & is in Club — 20; Likes science & not in Club — 21; Doesn't like science & in Club — 16; neither — 6. Given a student is in the Club, what is the probability they like science? Simplest form.

Answer (as a fraction)

Question 16

P(A) = 0.5, P(B) = 0.2 and P(A and B) = 0.1. Find P(A or B).

Answer