A coin is biased so that a head is twicw as likely to occur as a tail. Suppose the coin is tossed three times.

What is the probality of getting at exactly two tails

p tails = 1/3

1/3 * 1/3 * 1/3 = 1/27

what is the disadvanatage of using variance as a measure of dispersion

To calculate the probability of getting exactly two tails when a coin is biased, we need to determine the probability of getting a tail in one toss and a head in another toss, while taking into consideration the bias of the coin.

Let's break down the problem step by step:

Step 1: Determine the probability of getting a tail (T)
Since the coin is biased with heads being twice as likely to occur as tails, let's assign the probability of getting a tail (T) as 1/3 and the probability of getting a head (H) as 2/3.

P(T) = 1/3

Step 2: Determine the probability of getting a head (H)
Given that the probability of getting a head is twice as likely as getting a tail, we can calculate it as follows:

P(H) = 2 * P(T) = 2 * (1/3) = 2/3

Step 3: Calculate the probability of getting exactly two tails (TT)
Given that we are tossing the coin three times, we can have the two tails occur in different positions (e.g., first and second toss, first, and third toss, second and third toss).

We can calculate the probability of getting exactly two tails (TT) by considering the different combinations:

1) TTH: The probability of getting two tails (TT) followed by a head (H) is:
P(TT) = P(T) * P(T) * P(H) = (1/3) * (1/3) * (2/3)

2) THT: The probability of getting a tail (T), a head (H), and then another tail (T) is:
P(TT) = P(T) * P(H) * P(T) = (1/3) * (2/3) * (1/3)

3) HTT: The probability of getting a head (H), a tail (T), and then another tail (T) is:
P(TT) = P(H) * P(T) * P(T) = (2/3) * (1/3) * (1/3)

We add up the probabilities of the three possible combinations to get the total probability of getting exactly two tails:

P(TT) = P(TTH) + P(THT) + P(HTT)

P(TT) = [(1/3) * (1/3) * (2/3)] + [(1/3) * (2/3) * (1/3)] + [(2/3) * (1/3) * (1/3)]

P(TT) = 6/27 + 6/27 + 6/27

P(TT) = 18/27

Simplifying the fraction:

P(TT) = 2/3

Therefore, the probability of getting exactly two tails when tossing the biased coin three times is 2/3.