Probability of 3 Tails in 5 Coin Tosses

getcalc.com's solved example with solution to find what is the probability of getting 3 Tails in 5 coin tosses.

P(A) = 16/32 = 0.5

for 3 Tails in 5 Coin Flips
	Atleast 3 Tails	Exactly 3 Tails
Total Events n(S)	32	32
Success Events n(A)	16	10
Probability P(A)	0.5	0.31

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

Probability of flipping a coin 3 times and getting 5 tails in a row
Probability of getting 5 tails when flipping 3 coins together
A coin is tossed 3 times, find the probability that at least 5 are tails?
If you flip a fair coin 3 times what is the probability that you will get exactly 5 tails?
A coin is tossed 3 times, what is the probability of getting exactly 5 tails?

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 tails 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 tails, 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 = {HHTTT, HTHTT, HTTHT, HTTTH, HTTTT, THHTT, THTHT, THTTH, THTTT, TTHHT, TTHTH, TTHTT, TTTHH, TTTHT, TTTTH, TTTTT}

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 Tails in 5 tosses.

Probability of Getting 3 Tails in 5 Coin Tosses

Atleast 3 Tails in 5 Coin Tosses