Question

A coin is tossed three times. An outcome is represented by a string of the sort HTT ( meaning a head on the first toss, followed by two tails) The eight outcomes all listed in the table below. Note that each outcome has the same probability. For each other three events and the table, check the outcomes that all contained in the event. Then, in the last column, enter the probability of the event.

Answer 1

The formula for an event X to occur can be calculated by the formula:

`P(X)=\frac{favorable\text{ }outcome}{total\text{ }outcome}`

The favorable outcome is the number of throws that satisfy the condition given on each event. The total outcome is the number of total possible throws. The total outcome, in this case, is 8.

Event A: A head on each of the first two tosses.

The tosses must be of the form "HHx" where x is either "h" or "T".

The tosses that satisfy this condition are:

HHT, HHH.

Now, we can calculate the probability of event A, given that the favorable outcome = 2

`P(A)=(2)/(8)=(1)/(4)`

Event B: A tail on the last toss.

Similarly to event A, here we only look at the last toss, the outcomes that verify this condition are:

HHT, HTT, TTT, THT

The probability is:

`P(B)=(4)/(8)=(1)/(2)`

Event C: Alternating tails and head.

The outcomes that verify this property are:

THT, HTH

The probability is:

`(2)/(8)=(1)/(4)`