a fair (unbaised) coin is to be tossed 3 times. On each of the first 2 tosses the result is a head. What is the probability that the coin will land "heads" on the third toss?
2007-08-05 21:28:50 · 9 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
The answer is 1/2 = 50%. This is a typical example explaining a sequence of independent experiments (known as Bernoulli's sequence) where each single experiment can produce 2 alternatives (say, "success" and "unsuccess") and their probabilities are the same throughout the sequence (i.e. the outcome of each try is independent of the previous outcomes).
Assuming the coin is fair and it doesn't suffer malformations at each toss, the probabilities of both alternatives remain constantly 1/2. Otherwise we should conclude that the coin has some sort of "memory": it has "remembered" that the result had been twice a head, so now some "compensation" in its behaviour is necessary, leading the another alternative's probability to increase.
Don't You agree that the above sounds ridiculous?
2007-08-05 21:31:35 · answer #1 · answered by Duke 7 · 0⤊ 0⤋
In a fair coin or a normal coin, there are two outcomes : A Head and A Tail..
The probability of getting a Head is Therefore 1/2 = 50%
If you would have asked the probabilty of getting Three heads if three coins are tossed the results would have been different.....
But u have already stated what the outcomes of first two coins are and hence the probability of the third coin is calculated individually!
Hope it Helps!
2007-08-06 04:33:32 · answer #2 · answered by Nick 2 · 0⤊ 0⤋
1 in 2 or 50% the probability of heads in any individual toss is 1/2.
3 heads in 3 tosses in a row is 1/2*1/2*1/2 or 1 in 8 (1/8)
2007-08-06 04:38:11 · answer #3 · answered by 037 G 6 · 0⤊ 0⤋
given that the first two tosses show heads, there is only one toss left, and the probability of the coin shows heads is 1/2
2007-08-06 04:33:46 · answer #4 · answered by 7 · 0⤊ 0⤋
A coin-toss is a Markov process, meaning that the result of any toss is completely independent of the result of any other toss.
The odds of landing heads is always 50%.
2007-08-06 04:44:18 · answer #5 · answered by Anonymous · 0⤊ 0⤋
1/2
2007-08-06 04:31:44 · answer #6 · answered by Anonymous · 0⤊ 0⤋
The probability of getting 3 heads is different for the probability of getting heads GIVEN 2 heads
You are asking for the second, so that's why it's 1/2
Of you were asking for the first it would be 1/8
2007-08-06 04:37:56 · answer #7 · answered by Mutou Kazuki 2 · 0⤊ 0⤋
Answer is 1/8
Given the fact that a coin is tossed thrice then no of possibilities is 8 of which only one possibility would give the result as HHH.
2007-08-06 04:37:16 · answer #8 · answered by Pareshan Atma 2 · 0⤊ 2⤋
Answer: ratio = 1:1 or 1/2 or 0.5 or 50%
2007-08-10 03:47:20 · answer #9 · answered by Jun Agruda 7 · 2⤊ 0⤋