Question

Consider a coin that is weighted so that it is twice as likely to come up heads as tails. Answer the following questions using the Gaussian distribution description for the results of a series of coin tosses:a. What is the most likely outcome of a series of 2000 coin tosses using this biased coin?b. What is the relative probability of getting 1300 heads versus 1350 heads in a series of 2000 coin tosses using this coin?

Answer 1

Answer: 0.754

Explanation:

Given that, it is twice as likely to come up heads as tails in a coin ;

Let tail = T ; head = H

Total possible outcomes in the coin toss = 3

Number of heads = 2

Number of tails = 1

Probability = required outcome / Total possible outcomes

Then

P(T) = 1 / 3

P(H) = 2/3

What is the most likely outcome of a series of 2000 coin tosses using this biased coin?

Most likely outcome :

P = 2/3 = 0.667 ; n = 3

Using binomial distribution formula:

nCr * p^r * (1-p)^(n-r)

P=0 :

3C0 * 0.667^0 * (1 - 0.667)^(3-0) = 0.037

P=1 :

3C1 * 0.667^1 * (1 - 0.667)^(3-1) = 0.2218 = 0.222

P= 2 :

3C2 * 0.667^2 * (1 - 0.667)^(3-2)

= 0.444

b. What is the relative probability of getting 1300 heads versus 1350 heads in a series of 2000 coin tosses using this coin?