getcalc.com's solved example with solution to find what is the probability of getting 1 Head in 7 coin tosses.
P(A) = 127/128 = 0.99
for 1 Head in 7 Coin Flips | ||
---|---|---|
Atleast 1 Head | Exactly 1 Head | |
Total Events n(S) | 128 | 128 |
Success Events n(A) | 127 | 7 |
Probability P(A) | 0.99 | 0.05 |
The above probability of outcomes applicable to the below questions too.
The ratio of successful events A = 127 to the total number of possible combinations of a sample space S = 128 is the probability of 1 head in 7 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 1 head, if a coin is tossed seven times or 7 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 = {HHHHHHH, HHHHHHT, HHHHHTH, HHHHHTT, HHHHTHH, HHHHTHT, HHHHTTH, HHHHTTT, HHHTHHH, HHHTHHT, HHHTHTH, HHHTHTT, HHHTTHH, HHHTTHT, HHHTTTH, HHHTTTT, HHTHHHH, HHTHHHT, HHTHHTH, HHTHHTT, HHTHTHH, HHTHTHT, HHTHTTH, HHTHTTT, HHTTHHH, HHTTHHT, HHTTHTH, HHTTHTT, HHTTTHH, HHTTTHT, HHTTTTH, HHTTTTT, HTHHHHH, HTHHHHT, HTHHHTH, HTHHHTT, HTHHTHH, HTHHTHT, HTHHTTH, HTHHTTT, HTHTHHH, HTHTHHT, HTHTHTH, HTHTHTT, HTHTTHH, HTHTTHT, HTHTTTH, HTHTTTT, HTTHHHH, HTTHHHT, HTTHHTH, HTTHHTT, HTTHTHH, HTTHTHT, HTTHTTH, HTTHTTT, HTTTHHH, HTTTHHT, HTTTHTH, HTTTHTT, HTTTTHH, HTTTTHT, HTTTTTH, HTTTTTT, THHHHHH, THHHHHT, THHHHTH, THHHHTT, THHHTHH, THHHTHT, THHHTTH, THHHTTT, THHTHHH, THHTHHT, THHTHTH, THHTHTT, THHTTHH, THHTTHT, THHTTTH, THHTTTT, THTHHHH, THTHHHT, THTHHTH, THTHHTT, THTHTHH, THTHTHT, THTHTTH, THTHTTT, THTTHHH, THTTHHT, THTTHTH, THTTHTT, THTTTHH, THTTTHT, THTTTTH, THTTTTT, TTHHHHH, TTHHHHT, TTHHHTH, TTHHHTT, TTHHTHH, TTHHTHT, TTHHTTH, TTHHTTT, TTHTHHH, TTHTHHT, TTHTHTH, TTHTHTT, TTHTTHH, TTHTTHT, TTHTTTH, TTHTTTT, TTTHHHH, TTTHHHT, TTTHHTH, TTTHHTT, TTTHTHH, TTTHTHT, TTTHTTH, TTTHTTT, TTTTHHH, TTTTHHT, TTTTHTH, TTTTHTT, TTTTTHH, TTTTTHT, TTTTTTH, TTTTTTT}
S = 128
step 2 Find the expected or successful events A
A = {HHHHHHH, HHHHHHT, HHHHHTH, HHHHHTT, HHHHTHH, HHHHTHT, HHHHTTH, HHHHTTT, HHHTHHH, HHHTHHT, HHHTHTH, HHHTHTT, HHHTTHH, HHHTTHT, HHHTTTH, HHHTTTT, HHTHHHH, HHTHHHT, HHTHHTH, HHTHHTT, HHTHTHH, HHTHTHT, HHTHTTH, HHTHTTT, HHTTHHH, HHTTHHT, HHTTHTH, HHTTHTT, HHTTTHH, HHTTTHT, HHTTTTH, HHTTTTT, HTHHHHH, HTHHHHT, HTHHHTH, HTHHHTT, HTHHTHH, HTHHTHT, HTHHTTH, HTHHTTT, HTHTHHH, HTHTHHT, HTHTHTH, HTHTHTT, HTHTTHH, HTHTTHT, HTHTTTH, HTHTTTT, HTTHHHH, HTTHHHT, HTTHHTH, HTTHHTT, HTTHTHH, HTTHTHT, HTTHTTH, HTTHTTT, HTTTHHH, HTTTHHT, HTTTHTH, HTTTHTT, HTTTTHH, HTTTTHT, HTTTTTH, HTTTTTT, THHHHHH, THHHHHT, THHHHTH, THHHHTT, THHHTHH, THHHTHT, THHHTTH, THHHTTT, THHTHHH, THHTHHT, THHTHTH, THHTHTT, THHTTHH, THHTTHT, THHTTTH, THHTTTT, THTHHHH, THTHHHT, THTHHTH, THTHHTT, THTHTHH, THTHTHT, THTHTTH, THTHTTT, THTTHHH, THTTHHT, THTTHTH, THTTHTT, THTTTHH, THTTTHT, THTTTTH, THTTTTT, TTHHHHH, TTHHHHT, TTHHHTH, TTHHHTT, TTHHTHH, TTHHTHT, TTHHTTH, TTHHTTT, TTHTHHH, TTHTHHT, TTHTHTH, TTHTHTT, TTHTTHH, TTHTTHT, TTHTTTH, TTHTTTT, TTTHHHH, TTTHHHT, TTTHHTH, TTTHHTT, TTTHTHH, TTTHTHT, TTTHTTH, TTTHTTT, TTTTHHH, TTTTHHT, TTTTHTH, TTTTHTT, TTTTTHH, TTTTTHT, TTTTTTH}
A = 127
step 3 Find the probability
P(A) = Successful Events/Total Events of Sample Space
= 127/128
= 0.99
P(A) = 0.99
0.99 is the probability of getting 1 Head in 7 tosses.