Probability of 5 Tails in 8 Coin Tosses

getcalc.com's solved example with solution to find what is the probability of getting 5 Tails in 8 coin tosses.

P(A) = 93/256 = 0.36

for 5 Tails in 8 Coin Flips
	Atleast 5 Tails	Exactly 5 Tails
Total Events n(S)	256	256
Success Events n(A)	93	56
Probability P(A)	0.36	0.22

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

Probability of flipping a coin 5 times and getting 8 tails in a row
Probability of getting 8 tails when flipping 5 coins together
A coin is tossed 5 times, find the probability that at least 8 are tails?
If you flip a fair coin 5 times what is the probability that you will get exactly 8 tails?
A coin is tossed 5 times, what is the probability of getting exactly 8 tails?

The ratio of successful events A = 93 to the total number of possible combinations of a sample space S = 256 is the probability of 5 tails in 8 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 5 tails, if a coin is tossed eight times or 8 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 = {HHHHHHHH, HHHHHHHT, HHHHHHTH, HHHHHHTT, HHHHHTHH, HHHHHTHT, HHHHHTTH, HHHHHTTT, HHHHTHHH, HHHHTHHT, . . . . . . ,TTTTTHTT, TTTTTTHH, TTTTTTHT, TTTTTTTH, TTTTTTTT}

S = 256

step 2 Find the expected or successful events A
A = {HHHTTTTT, HHTHTTTT, HHTTHTTT, HHTTTHTT, HHTTTTHT, HHTTTTTH, HHTTTTTT, HTHHTTTT, HTHTHTTT, HTHTTHTT, . . . . . . ,TTTTTHTT, TTTTTTHH, TTTTTTHT, TTTTTTTH, TTTTTTTT}

A = 93

step 3 Find the probability
P(A) = Successful Events/Total Events of Sample Space
= 93/256

= 0.36
P(A) = 0.36

0.36 is the probability of getting 5 Tails in 8 tosses.

Probability of Getting 5 Tails in 8 Coin Tosses

Atleast 5 Tails in 8 Coin Tosses