Probability of Getting 3 Heads in 6 Coin Tosses
getcalc.com's solved example with solution to find what is the probability of getting 3 Heads in 6 coin tosses.
P(A) = 42/64 = 0.66
| for 3 Heads in 6 Coin Flips | ||
|---|---|---|
| Atleast 3 Heads | Exactly 3 Heads | |
| Total Events n(S) | 64 | 64 |
| Success Events n(A) | 42 | 20 |
| Probability P(A) | 0.66 | 0.31 |
The above probability of outcomes applicable to the below questions too.
- Probability of flipping a coin 3 times and getting 6 heads in a row
- Probability of getting 6 heads when flipping 3 coins together
- A coin is tossed 3 times, find the probability that at least 6 are heads?
- If you flip a fair coin 3 times what is the probability that you will get exactly 6 heads?
- A coin is tossed 3 times, what is the probability of getting exactly 6 heads?
Atleast 3 Heads in 6 Coin Tosses
The ratio of successful events A = 42 to the total number of possible combinations of a sample space S = 64 is the probability of 3 heads in 6 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 heads, if a coin is tossed fix times or 6 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 = {HHHHHH, HHHHHT, HHHHTH, HHHHTT, HHHTHH, HHHTHT, HHHTTH, HHHTTT, HHTHHH, HHTHHT, HHTHTH, HHTHTT, HHTTHH, HHTTHT, HHTTTH, HHTTTT, HTHHHH, HTHHHT, HTHHTH, HTHHTT, HTHTHH, HTHTHT, HTHTTH, HTHTTT, HTTHHH, HTTHHT, HTTHTH, HTTHTT, HTTTHH, HTTTHT, HTTTTH, HTTTTT, THHHHH, THHHHT, THHHTH, THHHTT, THHTHH, THHTHT, THHTTH, THHTTT, THTHHH, THTHHT, THTHTH, THTHTT, THTTHH, THTTHT, THTTTH, THTTTT, TTHHHH, TTHHHT, TTHHTH, TTHHTT, TTHTHH, TTHTHT, TTHTTH, TTHTTT, TTTHHH, TTTHHT, TTTHTH, TTTHTT, TTTTHH, TTTTHT, TTTTTH, TTTTTT}
S = 64
step 2 Find the expected or successful events A
A = {HHHHHH, HHHHHT, HHHHTH, HHHHTT, HHHTHH, HHHTHT, HHHTTH, HHHTTT, HHTHHH, HHTHHT, HHTHTH, HHTHTT, HHTTHH, HHTTHT, HHTTTH, HTHHHH, HTHHHT, HTHHTH, HTHHTT, HTHTHH, HTHTHT, HTHTTH, HTTHHH, HTTHHT, HTTHTH, HTTTHH, THHHHH, THHHHT, THHHTH, THHHTT, THHTHH, THHTHT, THHTTH, THTHHH, THTHHT, THTHTH, THTTHH, TTHHHH, TTHHHT, TTHHTH, TTHTHH, TTTHHH}
A = 42
step 3 Find the probability
P(A) = Successful Events/Total Events of Sample Space
= 42/64
= 0.66
P(A) = 0.66
0.66 is the probability of getting 3 Heads in 6 tosses.
Exactly 3 heads in 6 Coin Flips
The ratio of successful events A = 20 to total number of possible combinations of sample space S = 64 is the probability of 3 heads in 6 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 heads, if a coin is tossed fix times or 6 coins tossed together.
Solution :
Step by step workout
step 1 Find the total possible combinations of sample space S
S = {HHHHHH, HHHHHT, HHHHTH, HHHHTT, HHHTHH, HHHTHT, HHHTTH, HHHTTT, HHTHHH, HHTHHT, HHTHTH, HHTHTT, HHTTHH, HHTTHT, HHTTTH, HHTTTT, HTHHHH, HTHHHT, HTHHTH, HTHHTT, HTHTHH, HTHTHT, HTHTTH, HTHTTT, HTTHHH, HTTHHT, HTTHTH, HTTHTT, HTTTHH, HTTTHT, HTTTTH, HTTTTT, THHHHH, THHHHT, THHHTH, THHHTT, THHTHH, THHTHT, THHTTH, THHTTT, THTHHH, THTHHT, THTHTH, THTHTT, THTTHH, THTTHT, THTTTH, THTTTT, TTHHHH, TTHHHT, TTHHTH, TTHHTT, TTHTHH, TTHTHT, TTHTTH, TTHTTT, TTTHHH, TTTHHT, TTTHTH, TTTHTT, TTTTHH, TTTTHT, TTTTTH, TTTTTT}
S = 64
step 2 Find the expected or successful events A
A = {HHHTTT, HHTHTT, HHTTHT, HHTTTH, HTHHTT, HTHTHT, HTHTTH, HTTHHT, HTTHTH, HTTTHH, THHHTT, THHTHT, THHTTH, THTHHT, THTHTH, THTTHH, TTHHHT, TTHHTH, TTHTHH, TTTHHH}
A = 20
step 3 Find the probability
P(A) = Successful Events/Total Events of Sample Space
= 20/64
= 0.31
P(A) = 0.31
0.31 is the probability of getting exactly 3 Heads in 6 tosses.
