Question

two fair coins are thrown at the same time.The random variable X is the number of throws of the two coins required to obtain two tails at the same time.Find the probability that two tails are obtained for the first time on the 7th throw.​

Answer 1

Explanation:

when throwing 2 coins, there are 4 equally probable outcomes :

1 head 1 tail

1 tail 1 head

2 heads

2 tails

so, each outcome has a probability of 1/4.

the probability to not get 2 tails is the sum of the probabilities of 3 of these outcomes. so, it is

3/4.

to get 2 tails first at the xth attempt means that it did not happen at all x-1 attempts before.

that probability for that is

(3/4)^(x-1)

and then it happens. the probability for that is 1/4.

so, the total probability for that event is

(3/4)^(x-1) × 1/4 = (3^(x-1)) / (4^x)

so, for x = 7 that gives us a probability of

3⁶ / 4⁷ = 729 / 16384 = 0.044494629...