A gambler gives you a coin that he tells you is a \"trick\" coin. That is, the p

Question

A gambler gives you a coin that he tells you is a "trick" coin. That is, the probability of getting a head does not equal the probability of getting a tail. To use the coin to your advantage you need to know the probability of obtaining a head; i.e., p(H). a. How can you determine p(H)? b. Assuming you tossed the coin 5000 times and got 3500 heads, what would you estimate p(H) to be? c. What method of determining probability is this called? d. Using the binomial table, what is the probability that you can toss this coin 6 times and get 4 or more tails?

Explanation / Answer

a)

We can toss the coins n number of times n being a large number and find out the number od heads,

Dividing the number of heads by the number n will help us get the probability.

b)

estimate p(H) = 3500 / 5000 = 0.7

c)

This method is called the classical method.

d)

P(4 or more heads) =

P(4 heads) = 6C4 * 0.3*0.3*0.3*0.3*0.7*0.7 = 0.059535

P(5 heads) = 6C5 * 0.3*0.3*0.3*0.3*0.3*0.7 = 0.010206

P(6 heads) = 6C6 * 0.3*0.3*0.3*0.3*0.3*0.3 = 0.000729

                 = 0.07047

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