10th grade statistics and probability

Question 1

P(A) = 0.6, P(B) = 0.4 and P(A and B) = 0.3. Find P(A or B).

Answer 

Question 2

A card is drawn from a standard 52-card deck. Find the probability that it is a queen or a red card. Give a fraction in simplest form.

Answer (as a fraction)

Question 3

In a class, P(plays sport) = 0.6, P(plays an instrument) = 0.2 and P(sport or instrument) = 0.7. Find P(sport and instrument).

Answer 

Question 4

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

Answer 

Question 5

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

• A. A
• B. B
• C. They are equal

Question 6

A playlist has 6 pop songs and 6 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 7

Survey: Likes science & is in Club — 8; Likes science & not in Club — 24; Doesn't like science & in Club — 21; neither — 21. Given a student is in the Club, what is the probability they like science? Simplest form.

Answer (as a fraction)

Question 8

A box has 4 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 9

Some lengths have standard deviation 7 cm. Every length is multiplied by 5. What is the new standard deviation, in cm?

Answer 

Question 10

In a histogram, a bar covers a class of width 20 and has frequency density 1.5. What is the frequency?

Answer 

Question 11

P(A) = 0.5, P(B) = 0.4 and P(A and B) = 0.25. Are A and B independent?

• A. Yes
• B. No

Question 12

Set X: 21, 24, 27, 30, 33 Set Y: 11, 19, 27, 35, 43 Both have mean 27. Which set has the larger standard deviation?

• A. X
• B. Y
• C. They are equal

Question 13

Find the population standard deviation of: 4, 6, 4, 6

Answer 

Question 14

A bag has 3 red and 6 blue counters. Two are taken out without replacement. Find P(both red) as a fraction in simplest form.

Answer (as a fraction)

Question 15

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

Answer 

Question 16

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)