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

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) = x^{2} (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 4*4*4 = 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 )