Probability of Getting 7 Tails in 9 Coin Tosses

getcalc.com's solved example with solution to find what is the probability of getting 7 Tails in 9 coin tosses.

P(A) = 46/512 = 0.09

The ratio of successful events A = 46 to the total number of possible combinations of a sample space S = 512 is the probability of 7 tails in 9 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 7 tails, if a coin is tossed nine times or 9 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 = {HHHHHHHHH, HHHHHHHHT, HHHHHHHTH, HHHHHHHTT, HHHHHHTHH, HHHHHHTHT, HHHHHHTTH, HHHHHHTTT, HHHHHTHHH, HHHHHTHHT,    .    .    .    .    .    .    ,TTTTTTHTT, TTTTTTTHH, TTTTTTTHT, TTTTTTTTH, TTTTTTTTT}

S = 512

step 2 Find the expected or successful events A
A = {HHTTTTTTT, HTHTTTTTT, HTTHTTTTT, HTTTHTTTT, HTTTTHTTT, HTTTTTHTT, HTTTTTTHT, HTTTTTTTH, HTTTTTTTT, THHTTTTTT, THTHTTTTT, THTTHTTTT, THTTTHTTT, THTTTTHTT, THTTTTTHT, THTTTTTTH, THTTTTTTT, TTHHTTTTT, TTHTHTTTT, TTHTTHTTT, TTHTTTHTT, TTHTTTTHT, TTHTTTTTH, TTHTTTTTT, TTTHHTTTT, TTTHTHTTT, TTTHTTHTT, TTTHTTTHT, TTTHTTTTH, TTTHTTTTT, TTTTHHTTT, TTTTHTHTT, TTTTHTTHT, TTTTHTTTH, TTTTHTTTT, TTTTTHHTT, TTTTTHTHT, TTTTTHTTH, TTTTTHTTT, TTTTTTHHT, TTTTTTHTH, TTTTTTHTT, TTTTTTTHH, TTTTTTTHT, TTTTTTTTH, TTTTTTTTT}

A = 46

step 3 Find the probability
P(A) = Successful Events/Total Events of Sample Space
= 46/512

= 0.09
P(A) = 0.09

0.09 is the probability of getting 7 Tails in 9 tosses.