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

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.