Architecture

# A Fair Coin Is Flipped 9 Times. What Is The Probability Of Getting Exactly 6 Heads?

nadechworld.com”s solved example with solution to find what is the probability of getting 6 Heads in 9 coin tosses. P(A) = 130/512 = 0.25

Total Events n(S) 512 512
Success Events n(A) 130 84
Probability P(A) 0.25 0.16

The above probability of outcomes applicable to the below questions too.
Probability of flipping a coin 6 times and getting 9 heads in a row Probability of getting 9 heads when flipping 6 coins together A coin is tossed 6 times, find the probability that at least 9 are heads? If you flip a fair coin 6 times what is the probability that you will get exactly 9 heads? A coin is tossed 6 times, what is the probability of getting exactly 9 heads?

The ratio of successful events A = 130 to the total number of possible combinations of a sample space S = 512 is the probability of 6 heads 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 6 heads, 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.

SolutionStep by step workoutstep 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 = {HHHHHHHHH, HHHHHHHHT, HHHHHHHTH, HHHHHHHTT, HHHHHHTHH, HHHHHHTHT, HHHHHHTTH, HHHHHHTTT, HHHHHTHHH, HHHHHTHHT,……,TTHHHHTHH, TTHHHTHHH, TTHHTHHHH, TTHTHHHHH, TTTHHHHHH} A = 130 step 3 Find the probability P(A) = Successful Events/Total Events of Sample Space = 130/512 = 0.25 P(A) = 0.25 0.25 is the probability of getting 6 Heads in 9 tosses.

The ratio of successful events A = 84 to total number of possible combinations of sample space S = 512 is the probability of 6 heads in 9 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 6 heads, if a coin is tossed nine times or 9 coins tossed together.

Solution : Step by step workout step 1 Find the total possible combinations 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 = {HHHHHHTTT, HHHHHTHTT, HHHHHTTHT, HHHHHTTTH, HHHHTHHTT, HHHHTHTHT, HHHHTHTTH, HHHHTTHHT, HHHHTTHTH, HHHHTTTHH,……,TTHHHHTHH, TTHHHTHHH, TTHHTHHHH, TTHTHHHHH, TTTHHHHHH} A = 84 step 3 Find the probability P(A) = Successful Events/Total Events of Sample Space = 84/512 = 0.16 P(A) = 0.16 0.16 is the probability of getting exactly 6 Heads in 9 tosses.