SOLUTION: A fair coin is tossed nine times, with the result (H or T) of each flip noted.
How many outcomes does the experiment have?
How many outcomes are there where hea
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Question 1124876: A fair coin is tossed nine times, with the result (H or T) of each flip noted.
How many outcomes does the experiment have?
How many outcomes are there where heads comes up three times?
What is the probability of the outcome HHHTTTTTT?
What is the probability that heads comes up three times?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
2^9 = 512 outcomes
:
the binomial probability formula is
:
Probability (P) ( k successes in n trials ) = nCk * p^k * (1-p)^(n-k), where nCk = n!/k!(n-k)!, p is probability of success
:
if k = 3, then
:
P (3 heads in 9 trials) = 9C3 * (1/2)^3 * (1-(1/2))^(9-3) =
:
9!/3!(9-3)! * (1/8) * (1/64) =
:
(9*8*7/(3*2)) * (1/512) =
:
84/512
:
There are 84 outcomes where heads comes up three times
:
P of HHHTTTTTT = (1/2)^3 * (1/2)^6 = (1/8) * (1/64) = 1/512
:
P heads comes up three times is 84/512 = 21/128
:
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