When an unfair coin is tossed twice, the probability of getting one

hi buneul


whats difference between fair and unfair coin??...

thanks

In case of fair coin P(heads) = P(tails) = 1/2. If a coin is not fair, then the probabilities are different.

Am I correct to conclude that we can not find the probability of getting 3 tails on 4 tosses?

4C3 * x*x*x*(1-x) = 4/3 * x^2

We would have to know the individual probabilities of x and (1-x)?

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Yes, that's correct. The issue here is that the information is symmetric -- we learn that the probability of getting one head and one tail on two tosses is 1/3. If heads and tails were equally likely, that probability would instead be 1/2, and 1/3 is nowhere close to 1/2 in a probability setting, so it must be true that one of the two outcomes (heads or tails) is much more likely than the other. The problem is we don't know which. If you use the quadratic formula (which you don't need on the GMAT), the information in the stem tells us that on a single toss, we'll get one of the two results almost 80% of the time, and the other only about 20% of the time. If tails happens 80% of the time, it will be quite likely we get 3 tails on 4 tosses. But if tails only happens 20% of the time, it would be very rare to get 3 tails on 4 tosses. So your question has two possible answers. The question in this thread is only answerable because it asks for a symmetric result (2 heads, 2 tails) so we don't need to know which of the two outcomes is more likely.

Given: When an unfair coin is tossed twice, the probability of getting one tails and one heads is 1/3.
Asked: What is the probability of getting two heads and two tails if the coin is tossed 4 times?

Let probably of getting head be h and of getting tail be t
h = 1 - t

2C1 * h * t = 2ht = 1/3


Probability of getting two heads and two tails = 4C2 * h^2 t^2 = 6 * 1/6^2 = 1/6

IMO D

Isn't the x*(1-x) the probability of getting one heads and one tails on two coin tosses? If not, then what is x*(1-x) in this scenario? How should I think about x*(1-x)?