Question

Consider a fair coin which when tossed results in either heads (H) or tails (T). If the coin is tossed TWO times 1. List all possible outcomes. (Order matters here. So, HT and TH are not the same outcome.) 2. Write the sample space. 3. List ALL possible events and compute the probability of each event, assuming that the probability of each possible outcome from part (a) is equal. (Keep in mind that there should be many more events than outcomes and not all events will have the same probability.)

Answer 1

Sample space = {(T,T), (T,H), (HT), (HH)}

Explanation:

We are given a fair coin which when tossed one times either gives heads(H) or tails(T).

Now, the same coin is tossed two times.

1) All the possible outcomes

Tails followed by tails

Rails followed by heads

Heads followed by a tail

Heads followed by heads

2) Sample space

{(T,T), (T,H), (HT), (HH)}

3) Formula:

`Probability = \displaystyle\frac{\text{Favourable outcome}}{\text{Total number of outcome}}`

Using the above formula, we can compute the following probabilities.

Probability((T,T)) =
`(1)/(4)`

Probability((T,H)) =
`(1)/(4)`

Probability((H,T)) =
`(1)/(4)`

Probability((H, H)) =
`(1)/(4)`

Probability(Atleast one tails) =
`(3)/(4)`

Probability(Atleast one heads) =
`(3)/(4)`

Probability(Exactly one tails) =
`(2)/(4)`

Probability(Exactly one heads) =
`(2)/(4)`