# Probability of Getting 3 Heads in 5 Coin Tosses

## Atleast 3 Heads in 5 Coin Tosses

The ratio of successful events A = 16 to the total number of possible combinations of a sample space S = 32 is the probability of 3 heads in 5 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 five times or 5 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 = {HHHHH, HHHHT, HHHTH, HHHTT, HHTHH, HHTHT, HHTTH, HHTTT, HTHHH, HTHHT, HTHTH, HTHTT, HTTHH, HTTHT, HTTTH, HTTTT, THHHH, THHHT, THHTH, THHTT, THTHH, THTHT, THTTH, THTTT, TTHHH, TTHHT, TTHTH, TTHTT, TTTHH, TTTHT, TTTTH, TTTTT}

S = 32

step 2 Find the expected or successful events A

A = {HHHHH, HHHHT, HHHTH, HHHTT, HHTHH, HHTHT, HHTTH, HTHHH, HTHHT, HTHTH, HTTHH, THHHH, THHHT, THHTH, THTHH, TTHHH}

A = 16

step 3 Find the probability

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

= 16/32

= 0.5

P(A) = 0.5

0.5 is the probability of getting 3 Heads in 5 tosses.

## Exactly 3 heads in 5 Coin Flips

The ratio of successful events A = 10 to total number of possible *combinations* of sample space S = 32 is the probability of 3 heads in 5 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 five times or 5 coins tossed together.

**Solution :**__Step by step workout__

step 1 Find the total possible combinations of sample space S

S = {HHHHH, HHHHT, HHHTH, HHHTT, HHTHH, HHTHT, HHTTH, HHTTT, HTHHH, HTHHT, HTHTH, HTHTT, HTTHH, HTTHT, HTTTH, HTTTT, THHHH, THHHT, THHTH, THHTT, THTHH, THTHT, THTTH, THTTT, TTHHH, TTHHT, TTHTH, TTHTT, TTTHH, TTTHT, TTTTH, TTTTT}

S = 32

step 2 Find the expected or successful events A

A = {HHHTT, HHTHT, HHTTH, HTHHT, HTHTH, HTTHH, THHHT, THHTH, THTHH, TTHHH}

A = 10

step 3 Find the probability

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

= 10/32

= 0.31

P(A) = 0.31

0.31 is the probability of getting exactly 3 Heads in 5 tosses.