Probability of Simple Events — Challenge

Probability is a fraction: what you want over everything that could happen — as long as every outcome is equally likely.

What these problems cover

These questions use 2 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.

Problem 1

A fair six-sided die is rolled once. What is the probability of rolling a 4?

  1. 16
  2. 14
  3. 23
  4. 13
  5. 12
Worked answer

16

There are six equally likely outcomes and exactly one of them is a 4.

So the probability is 16.

Problem 2

A bag holds 3 red counters and 5 blue counters. One is drawn at random. What is the probability it is red?

  1. 38
  2. 35
  3. 58
  4. 13
  5. 18
Worked answer

38

The bag holds 3+5 = 8 counters in total.

Three of the eight are red, so the probability is 38.

The answer 35 would come from comparing red with blue rather than with the whole bag.

Problem 3

A spinner has eight equal sectors numbered 1 to 8. What is the probability of landing on a prime number?

  1. 18
  2. 38
  3. 12
  4. 58
  5. 34
Worked answer

12

The primes from 1 to 8 are 2, 3, 5 and 7. That is four of them.

Note that 1 is not prime, because a prime has exactly two factors.

So the probability is 48 = 12.

Problem 4

A fair coin is flipped once. What is the probability it shows heads?

  1. 14
  2. 13
  3. 12
  4. 23
  5. 1
Worked answer

12

There are two equally likely outcomes, heads and tails.

One of the two is heads, so the probability is 12.

Problem 5

A jar holds 20 marbles and 12 of them are green. One marble is drawn at random. What is the probability it is not green?

  1. 15
  2. 25
  3. 35
  4. 23
  5. 45
Worked answer

25

If 12 of the 20 are green then 20-12 = 8 are not.

The probability of drawing one of those is 820 = 25.

Equivalently, 1-1220 = 1-35 = 25.

Problem 6

A fair six-sided die is rolled. What is the probability the result is greater than 4?

  1. 16
  2. 13
  3. 12
  4. 23
  5. 56
Worked answer

13

The results greater than 4 are 5 and 6, so two outcomes qualify.

The probability is 26 = 13. Note that 4 itself does not count.

Problem 7

Tickets numbered 1 to 30 are placed in a box and one is drawn at random. What is the probability its number is a multiple of 5?

  1. 110
  2. 16
  3. 15
  4. 13
  5. 25
Worked answer

15

The multiples of 5 up to 30 are 5, 10, 15, 20, 25, 30, which is six tickets.

The probability is 630 = 15.

Problem 8

A bag holds 4 white counters and 6 black counters. What is the probability that a counter drawn at random is white?

  1. 25
  2. 35
  3. 23
  4. 14
  5. 110
Worked answer

25

There are 4+6 = 10 counters altogether.

Four are white, so the probability is 410 = 25.

Problem 9

An event has probability 34. What is that as a percentage?

  1. 25%
  2. 50%
  3. 60%
  4. 75%
  5. 80%
Worked answer

75%

To write a fraction as a percentage, express it in hundredths.

34 = 75100 = 75%.

Problem 10

A spinner has five equal sectors and two of them are red. What is the probability of landing on red?

  1. 15
  2. 25
  3. 35
  4. 12
  5. 23
Worked answer

25

All five sectors are equally likely and two of them are red.

So the probability is 25.

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