For example, if one tosses a coin 3 times, what are the odds that 1 toss will be "heads"?
2006-12-06 14:55:40 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Work it through chronologically:
The odds of getting heads the first time is 1/3...
The odds of getting it the second toss is 1/3...
So, the odds of getting it the first toss and then the second toss is 1/3 of 1/3, which is 1/9.
Then the odds of getting heads on the third toss is 1/3.. so the odds of getting heads all 3 times is 1/3 * 1/3 * 1/3 = 1/27
I could have just said "multiply", but you need to think it through, otherwise you'll make mistakes on more complex examples.
2006-12-06 15:02:02 · answer #1 · answered by Edward M 2 · 0⤊ 0⤋
Probability is the ratio of the # of successes / # outcomes.
you need to determine the outcomes of tossing the coin 3 times.
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT
or just multiply 2 choices x 2 choice x 2 choices
Then, count the number of successes. If you mean by the statement "1 toss will be a head" than any H occurs, this happens in all but one case, TTT.
so the P(1 toss will be a head) = 1/8
If you mean that exactly one head occurs, then there are 3 times this happens.
you get the idea.
2006-12-06 15:01:47 · answer #2 · answered by grand_nanny 5 · 0⤊ 0⤋
find the probability that the first toss is a heads and the other 2 are tails and add that to the probability that the second toss is a heads and the other 2 are tails and add that to the probability that the third toss is a head and the other 2 are tails
you get 1/8 + 1/8 + 1/8 = 3/8
2006-12-06 14:58:53 · answer #3 · answered by socialistmath 2 · 0⤊ 0⤋
1/8
You multiply the probability of each individual event, in this case, 1/2 * 1/2 * 1/2 = 1/8 is the probablity that you will get heads 3 out of 3 times flipping a coin. To see that this is true look at the possible outcomes, and you'll see only 1 of the 8 is HHH:
HHH
HTH
HTT
HHT
TTT
THT
THH
TTH
2006-12-06 15:02:16 · answer #4 · answered by NvestR3322 2 · 0⤊ 0⤋
The odds are different if you say "at least one is heads", and "exactly one is heads". The most direct way to compute odds is to look at all the possible outcomes, count the total, and divide that total into the special cases in question. With 3 coin throws, there are 8 possible outcomes, or histories. There are 7 possible "at least one is heads" outcomes, and there are only 3 possible "exactly one is heads" outcomes, so the respective odds would be 7/8, and 3/8. When in doubt in figuring out probability, always look at the total number of possible outcomes first.
2006-12-06 15:00:17 · answer #5 · answered by Scythian1950 7 · 0⤊ 0⤋