Probability of Getting 3 Tails in 5 Coin Tosses
getcalc.com's solved example with solution to find what is the probability of getting 3 Tails in 5 coin tosses.
P(A) = 16/32 = 0.5
| for 3 Tails in 5 Coin Flips | ||
|---|---|---|
| Atleast 3 Tails | Exactly 3 Tails | |
| Total Events n(S) | 32 | 32 |
| Success Events n(A) | 16 | 10 |
| Probability P(A) | 0.5 | 0.31 |
The above probability of outcomes applicable to the below questions too.
- Probability of flipping a coin 3 times and getting 5 tails in a row
- Probability of getting 5 tails when flipping 3 coins together
- A coin is tossed 3 times, find the probability that at least 5 are tails?
- If you flip a fair coin 3 times what is the probability that you will get exactly 5 tails?
- A coin is tossed 3 times, what is the probability of getting exactly 5 tails?
Atleast 3 Tails in 5 Coin Tosses
The ratio of successful events A = 16 to the total number of possible combinations of a sample space S = 32 is the probability of 3 tails in 5 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 tails, if a coin is tossed five times or 5 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 = {HHHHH, HHHHT, HHHTH, HHHTT, HHTHH, HHTHT, HHTTH, HHTTT, HTHHH, HTHHT, HTHTH, HTHTT, HTTHH, HTTHT, HTTTH, HTTTT, THHHH, THHHT, THHTH, THHTT, THTHH, THTHT, THTTH, THTTT, TTHHH, TTHHT, TTHTH, TTHTT, TTTHH, TTTHT, TTTTH, TTTTT}
S = 32
step 2 Find the expected or successful events A
A = {HHTTT, HTHTT, HTTHT, HTTTH, HTTTT, THHTT, THTHT, THTTH, THTTT, TTHHT, TTHTH, TTHTT, TTTHH, TTTHT, TTTTH, TTTTT}
A = 16
step 3 Find the probability
P(A) = Successful Events/Total Events of Sample Space
= 16/32
= 0.5
P(A) = 0.5
0.5 is the probability of getting 3 Tails in 5 tosses.
Exactly 3 tails in 5 Coin Flips
The ratio of successful events A = 10 to total number of possible combinations of sample space S = 32 is the probability of 3 tails in 5 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 tails, if a coin is tossed five times or 5 coins tossed together.
Solution :
Step by step workout
step 1 Find the total possible combinations of sample space S
S = {HHHHH, HHHHT, HHHTH, HHHTT, HHTHH, HHTHT, HHTTH, HHTTT, HTHHH, HTHHT, HTHTH, HTHTT, HTTHH, HTTHT, HTTTH, HTTTT, THHHH, THHHT, THHTH, THHTT, THTHH, THTHT, THTTH, THTTT, TTHHH, TTHHT, TTHTH, TTHTT, TTTHH, TTTHT, TTTTH, TTTTT}
S = 32
step 2 Find the expected or successful events A
A = {HHTTT, HTHTT, HTTHT, HTTTH, THHTT, THTHT, THTTH, TTHHT, TTHTH, TTTHH}
A = 10
step 3 Find the probability
P(A) = Successful Events/Total Events of Sample Space
= 10/32
= 0.31
P(A) = 0.31
0.31 is the probability of getting exactly 3 Tails in 5 tosses.
