# Probability of Getting 3 Heads in 6 Coin Tosses

getcalc.com's solved example with solution to find what is the probability of getting 3 Heads in 6 coin tosses.

P(A) = 42/64 = 0.66

for 3 Heads in 6 Coin Flips | ||
---|---|---|

Atleast 3 Heads | Exactly 3 Heads | |

Total Events n(S) | 64 | 64 |

Success Events n(A) | 42 | 20 |

Probability P(A) | 0.66 | 0.31 |

The above probability of outcomes applicable to the below questions too.

- Probability of flipping a coin 3 times and getting 6 heads in a row
- Probability of getting 6 heads when flipping 3 coins together
- A coin is tossed 3 times, find the probability that at least 6 are heads?
- If you flip a fair coin 3 times what is the probability that you will get exactly 6 heads?
- A coin is tossed 3 times, what is the probability of getting exactly 6 heads?

## Atleast 3 Heads in 6 Coin Tosses

The ratio of successful events A = 42 to the total number of possible combinations of a sample space S = 64 is the probability of 3 heads in 6 coin tosses. Users may refer the below solved example work with steps to learn how to find what is the probability of getting at-least 3 heads, if a coin is tossed fix times or 6 coins tossed together. Users may refer this tree diagram to learn *how to find all the possible combinations of sample space* for flipping a coin one, two, three or four times.

**Solution**__Step by step workout__

step 1 Find the total possible events of sample space S

S = {HHHHHH, HHHHHT, HHHHTH, HHHHTT, HHHTHH, HHHTHT, HHHTTH, HHHTTT, HHTHHH, HHTHHT, HHTHTH, HHTHTT, HHTTHH, HHTTHT, HHTTTH, HHTTTT, HTHHHH, HTHHHT, HTHHTH, HTHHTT, HTHTHH, HTHTHT, HTHTTH, HTHTTT, HTTHHH, HTTHHT, HTTHTH, HTTHTT, HTTTHH, HTTTHT, HTTTTH, HTTTTT, THHHHH, THHHHT, THHHTH, THHHTT, THHTHH, THHTHT, THHTTH, THHTTT, THTHHH, THTHHT, THTHTH, THTHTT, THTTHH, THTTHT, THTTTH, THTTTT, TTHHHH, TTHHHT, TTHHTH, TTHHTT, TTHTHH, TTHTHT, TTHTTH, TTHTTT, TTTHHH, TTTHHT, TTTHTH, TTTHTT, TTTTHH, TTTTHT, TTTTTH, TTTTTT}

S = 64

step 2 Find the expected or successful events A

A = {HHHHHH, HHHHHT, HHHHTH, HHHHTT, HHHTHH, HHHTHT, HHHTTH, HHHTTT, HHTHHH, HHTHHT, HHTHTH, HHTHTT, HHTTHH, HHTTHT, HHTTTH, HTHHHH, HTHHHT, HTHHTH, HTHHTT, HTHTHH, HTHTHT, HTHTTH, HTTHHH, HTTHHT, HTTHTH, HTTTHH, THHHHH, THHHHT, THHHTH, THHHTT, THHTHH, THHTHT, THHTTH, THTHHH, THTHHT, THTHTH, THTTHH, TTHHHH, TTHHHT, TTHHTH, TTHTHH, TTTHHH}

A = 42

step 3 Find the probability

P(A) = Successful Events/Total Events of Sample Space

= 42/64

= 0.66

P(A) = 0.66

0.66 is the probability of getting 3 Heads in 6 tosses.

## Exactly 3 heads in 6 Coin Flips

The ratio of successful events A = 20 to total number of possible *combinations* of sample space S = 64 is the probability of 3 heads in 6 coin tosses. Users may refer the below detailed solved example with step by step calculation to learn how to find what is the probability of getting exactly 3 heads, if a coin is tossed fix times or 6 coins tossed together.

**Solution :**__Step by step workout__

step 1 Find the total possible combinations of sample space S

S = {HHHHHH, HHHHHT, HHHHTH, HHHHTT, HHHTHH, HHHTHT, HHHTTH, HHHTTT, HHTHHH, HHTHHT, HHTHTH, HHTHTT, HHTTHH, HHTTHT, HHTTTH, HHTTTT, HTHHHH, HTHHHT, HTHHTH, HTHHTT, HTHTHH, HTHTHT, HTHTTH, HTHTTT, HTTHHH, HTTHHT, HTTHTH, HTTHTT, HTTTHH, HTTTHT, HTTTTH, HTTTTT, THHHHH, THHHHT, THHHTH, THHHTT, THHTHH, THHTHT, THHTTH, THHTTT, THTHHH, THTHHT, THTHTH, THTHTT, THTTHH, THTTHT, THTTTH, THTTTT, TTHHHH, TTHHHT, TTHHTH, TTHHTT, TTHTHH, TTHTHT, TTHTTH, TTHTTT, TTTHHH, TTTHHT, TTTHTH, TTTHTT, TTTTHH, TTTTHT, TTTTTH, TTTTTT}

S = 64

step 2 Find the expected or successful events A

A = {HHHTTT, HHTHTT, HHTTHT, HHTTTH, HTHHTT, HTHTHT, HTHTTH, HTTHHT, HTTHTH, HTTTHH, THHHTT, THHTHT, THHTTH, THTHHT, THTHTH, THTTHH, TTHHHT, TTHHTH, TTHTHH, TTTHHH}

A = 20

step 3 Find the probability

P(A) = Successful Events/Total Events of Sample Space

= 20/64

= 0.31

P(A) = 0.31

0.31 is the probability of getting exactly 3 Heads in 6 tosses.