What answer did you get and how did you get it?
So I don’t know LateX so I’ll type in text hope that’s helpful
Statements:
- H * H * T = \frac{3}{64}
- T * T * H = \frac{9}{64}
Taking the first statement and substituting
T = \frac{3}{64*H*H}
Substituting value of T in 2nd eq.
\frac{3}{64*H*H} * \frac{3}{64*H*H} * H = \frac{9}{64}
Solve this and you’ll get H= 1/4
How did you get 1/4?
Hey guys, what is the proper solution to this problem ?
I would say that arohanjit’s solution is fine, alternative Greg has solved it in the Medium quant class that you may check. And Probability with baited coin help please! - #5 by hmulavekar
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Thank you very much 
A biased coin (that is, one with an unequal chance of getting heads or tails) is tossed three times in a row. If the probability of getting two heads in a row and then a tails is
3/64 and the probability of getting two tails in a row and then a heads is
9/64 , what is the probability of getting a heads on the fourth flip of the coin?
Let P(H) = x
P(T) = 1 - x
P(HHT) = x2 (1-x) = 3/64
P(TTH) = (x-1)2 x = 9/64
dividing the two equations:
x/(1-x) = 3/9
9x = 3 - 3x
12x = 3
x = 3/12 or P(H) = 1/4
As P(H) is the same for each flip, ans = 1/4
u need to do combinations which is HHHH+3*(HHTH)+3*(TTHH)+(TTTH) and find the answer as p(H)=1/4 p(T)=3/4
As Greg told in the live session also, the more astute GRE candidate would recognize that the denominators of the probabilities mentioned in the question in 64 and the coin is tossed 3 times hence we could say with a definite certainty that the probability of getting heads or tails in this question must contain 4 in its denominator (as 444 = 64)i.e. x/4 where x is any integer.
We have to also remember that if p(H) = x then p(T)=1-x, with the help of all this information we can assume the value of x and try to get values mentioned in the question
for example we can say that
let probability of head occuring is —x,
so tail prob is (1-x)
1> two heads and tail------x \times x \times (1-x)=3/64
2>two tails and head-------(1-x)\times(1-x)\times x=9/64
then solve equations .you will get x value i think its 1/4
What are the x values you get after solving the equation? I’m getting 1/4 as well as 3/4
x(head) will be 1/4 , (1-x) will be 3/4 (this is the value for tail )
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