Probability and Sample Spaces

What is the sample space for an experiment?

The set of all possible outcomes

What is the sample space for flipping one coin?

{H, T}

What is the probability of getting Heads (H) when flipping a fair coin?

1/2

What is the probability of flipping heads with a fair coin?

P(H) = |{H}| / |{H, T}| = 1/2 = 0.5

What is the sample space for flipping two coins?

{(H,H), (H,T), (T,H), (T,T)}

What is the probability of getting (H,H) when flipping two coins?

1/4 (1 outcome out of 4)

What is the probability of getting (T,T) when flipping two coins?

0.25 (1 outcome out of 4)

What is the sample space for rolling a single die?

{1, 2, 3, 4, 5, 6}

What is the probability of rolling a 3 on a single die?

1/6

How many outcomes are there in the sample space for rolling two six-sided dice?

36 (6 x 6)

What is the probability of rolling (1,1) with two dice?

1/36

How many ways can the sum of two dice equal 4?

3: (1,3), (2,2), (3,1)

Which sum has the highest probability in the distribution for two dice?

7 (6 ways out of 36)

What is the sample space for rolling a four-sided die?

{1, 2, 3, 4}

What is the probability of rolling a 2 on a four-sided die?

1/4

How many outcomes are in the sample space for rolling 2d4?

16 (4 x 4)

What is the probability of getting a sum of 2 when rolling 2d4?

1/16 (only (1,1))

What is the probability of getting a sum of 8 when rolling 2d4?

1/16 (only (4,4))

Which sum has the highest probability when rolling 2d4?

5 (4 ways out of 16)

How many outcomes are in the sample space for rolling 3d4?

64 (4 x 4 x 4)

How many ways can the sum equal 3 when rolling 3d4?

1 (only (1,1,1))