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Brain Teasers

Chance would be a fine thing.

Fair coins, simple dice, and clearly stated assumptions.

Ten questions, with the answers explained. Try them in your head, then open each answer when you're ready.

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QUESTION 1 / 10

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

  • 1 in 3
  • 1 in 6
  • 1 in 2
  • 1 in 12
Show answer & explanation+

1 in 6

There is one six among six equally likely outcomes.

QUESTION 2 / 10

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

  • 1
  • 1/4
  • 1/3
  • 1/2
Show answer & explanation+

1/2

The two outcomes are equally likely, so heads has probability one half.

QUESTION 3 / 10

A bag contains three red and one blue token. One is drawn at random. What is the chance it is blue?

  • 1/2
  • 3/4
  • 1/4
  • 1/3
Show answer & explanation+

1/4

One of the four equally likely tokens is blue.

QUESTION 4 / 10

A fair die is rolled. What is the chance of an even number?

  • 1/2
  • 1/6
  • 1/3
  • 2/3
Show answer & explanation+

1/2

Three outcomes, 2, 4, and 6, are even, out of six outcomes.

QUESTION 5 / 10

Two fair coin flips are independent. What is the chance both are heads?

  • 1/2
  • 3/4
  • 1/3
  • 1/4
Show answer & explanation+

1/4

The four equally likely sequences are HH, HT, TH, and TT. Only HH qualifies.

QUESTION 6 / 10

A bag has only green tokens. What is the chance of drawing a red token?

  • Zero
  • One half
  • One third
  • One
Show answer & explanation+

Zero

There are no red tokens to draw.

QUESTION 7 / 10

A fair die is rolled. What is the chance of a number greater than four?

  • 2/3
  • 1/2
  • 1/3
  • 1/6
Show answer & explanation+

1/3

Only 5 and 6 qualify: two of six outcomes, or one third.

QUESTION 8 / 10

A jar has two yellow and three purple beads. One is drawn at random. What is the chance of yellow?

  • 3/5
  • 1/5
  • 2/5
  • 1/2
Show answer & explanation+

2/5

Two of the five beads are yellow.

QUESTION 9 / 10

After five heads in a row on a fair coin, what is the chance the next independent flip is heads?

  • 1/6
  • 1/32
  • Zero
  • 1/2
Show answer & explanation+

1/2

Earlier results do not change the next independent fair flip.

QUESTION 10 / 10

A spinner has four equal sectors labeled A, B, C, D. What is the chance of landing on A or B?

  • 1/4
  • 1/2
  • 1
  • 3/4
Show answer & explanation+

1/2

Two of the four equally likely sectors qualify.

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