<PRE><B>Question 1082101</B>
Let Probability(P) of getting a tail on a toss = x
:
Let P of getting a head on a toss = 2x
:
we know the sum of the probabilities = 1
:
x + 2x = 1
:
x = 1/3
:
P of getting a tail on a toss = 1/3
P of getting a head on a toss = 2/3
:
i)  there are 2^4 possible combinations
HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT,
THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT 
:
Note that there is no difference between tossing 1 coin 4 times and tossing
4 coins once
:
We use the binomial probability for ii and iv
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ii) P(at least 2 heads) = 1 - P(0 heads) - P(1 head)
Note P(k successes in n trials) = nCk * p^k * (1-p)^n-k, where p = 2/3, n = 4,
4Ck = 4! / (k! * (n-k)!
P(at least 2 heads) = 1 - 0.01 - 0.10 = 0.89
:
iii) P(of 3 heads) = 0.40
:
iv)  P(at most 4 heads) = 1 - P(0 heads)
P(at most 4 heads) = 1 - 0.01 = 0.99
:
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