Coin tossing probabilities

A fair coin is tossed 5 times.

What is the probability of getting at least three heads on consecutive tosses?

• 4/32 = 1/8

• 8/32 = 1/4

• 7/24

• 10/32 = 5/16

• 15/32

Answer explanation

There are 2×2×2×2×2 = 2⁵ = 32 different outcomes for tossing a coin 5 times.

There are 8 different outcomes with at least 3 heads on consecutive tosses, in other words, 3 heads in a row.

{HHHHH, HHHHT, HHHTH, HHHTT, HTHHH, THHHH, THHHT, TTHHH}

So 8/32 = 1/4 probability.

If a certain coin is flipped, the probability that the coin will land heads is 1/2.

If the coin is flipped 5 times, what is the probability that it will land heads up on the first 3 flips and not on the last 2 flips?

• 3/5

• 1/2

• 1/5

• 1/8

• 1/32

Answer explanation

Total possible outcomes for flipping a coin 5 times is 2×2×2×2×2 = 2⁵ = 32 possible outcomes.

Only 1 outcome is three heads then two not head. {HHHTT}

P(HHHTT) = 1/32

When tossed, a certain coin has equal probability of landing on either side.

If the coin is tossed 3 times, what is the probability that it will land on the same side each time?

• 1/8

• 1/4

• 1/3

• 3/8

• 1/2

Answer explanation

Total possible outcomes of flipping a fair coin 3 times would be 2×2×2 = 2³ = 8 different outcomes.

There are only 2 outcomes where the coin shows the same side for all three flips are {HHH, TTT}.

P(HHH or TTT) = 2/8 = 1/4

What is the probability of flipping a fair coin two times and the coin landing on tails on both flips?

• 1/8 = 0.125 = 12.5%

• 1/4 = 0.25 = 25%

• 1/2 = 0.5 = 50%

• 3/8 = 0.375 = 37.5%

• 3/4 = 0.75 = 75%

Answer explanation

There are 2×2 = 2² = 4 different outcomes for flipping a coin twice.

{HH, HT, TH, TT}

Only one of these outcomes show all tails. {TT}

P(TT) = 1/4 = 0.25 = 25%

Kevin flips a coin four times.

What is the probability that he gets heads on at least one of the four flip?

• 1/16

• 1/4

• 3/4

• 13/16

• 15/16

Answer explanation

There are 2×2×2×2 = 2⁴ = 16 different outcomes when flipping a coin 4 times.

There is only 1 way to not get a heads {TTTT}.

So the probability of getting at least one head is the complement of not getting any heads.

1 - P(TTTT) = 1 - 1/16 = 15/16

Which event is more likely, rolling a six sided number cube and getting an even number, or tossing a coin and having it land heads up?

• even number on the number cube

• heads up with a coin toss

• equally likely

• I don't know - I don't have any dice or money

• odd number on the number cube

Answer explanation

There are 6 outcomes on a six-sided number cube.

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

Three of these outcomes are even. {2, 4, 6}

P(even) = 3/6 = 1/2

There are 2 outcomes on a coin. {H, T}

One of these outcomes is heads. {H}

P(heads) = 1/2

These events are equally likely.

A certain fair coin with heads on one side and tails on the other is flipped three times.

What is the probability of flipping 2 tails and 1 head, in any order?

• 1/8

• 1/3

• 3/8

• 5/8

• 2/3

Answer explanation

There are 2×2×2 = 2³ = 8 different outcomes for flipping the coin 3 times.

There are 3 different ways to get 2 heads and a tail.

{HHT, HTH, THH}

So probability is 3/8.