# Probability of Getting 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 TailsExactly 3 Tails
Total Events n(S)3232
Success Events n(A)1610
Probability P(A)0.50.31

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?

## Atleast 3 Tails 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 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.

## Exactly 3 tails 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 tails 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 tails, 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 = {HHTTT, HTHTT, HTTHT, HTTTH, THHTT, THTHT, THTTH, TTHHT, TTHTH, TTTHH}

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 Tails in 5 tosses.