A coin is tossed twice and comes up heads both times. Someone says, “There’s something wrong with this coin. A coin is supposed to come up heads only half the time, not every time.”

a. Is it reasonable to conclude that something is wrong with the coin? Explain.

b. If the coin came up heads 100 times in a row, would it be reasonable to conclude that something is wrong with the coin? Explain.

Solution 4SE

Step1 of 3:

We have fair coin and it is tossed twice and comes up heads both times. Someone says, “There’s something wrong with this coin. A coin is supposed to come up heads only half the time, not every time.”

We need to check,

a).Is it reasonable to conclude that something is wrong with the coin? Explain.

b).If the coin came up heads 100 times in a row, would it be reasonable to conclude that something is wrong with the coin? Explain.

Step2 of 3:

a).

Consider A fair coin X.

The possible number of outcomes are S = {H,T}

Probability of getting Head is given by

P(H) =

=

Hence,P(H) = ½.

Therefore, Probability of getting Head is ½.

Similarly,

Probability of getting Tail is given by

P(T) =

...