Sample Space and Possible Outcomes:
The total number of possible outcomes in the sample space is (2^4 = 16), since there are 4 tosses of the coin.
We can have the following outcomes: 0 heads, 1 head, 2 heads, 3 heads, or 4 heads.
Calculating Probabilities:
(P(X=0) =
(P(X=1) =
(P(X=2) =
(P(X=3) =
To calculate the probabilities, we need to determine the number of ways each outcome can occur and divide by the total number of possible outcomes.
1. P(X=0) - This means getting 0 heads in 4 coin tosses. There is only 1 way this can happen (getting tails on all 4 tosses). So, P(X=0) = 1/16.
2. P(X=1) - This means getting 1 head in 4 coin tosses. There are 4 ways this can happen (H T T T, T H T T, T T H T, T T T H). So, P(X=1) = 4/16 = 1/4.
3. P(X=2) - This means getting 2 heads in 4 coin tosses. There are 6 ways this can happen (H H T T, H T H T, H T T H, T H H T, T H T H, T T H H). So, P(X=2) = 6/16 = 3/8.
4. P(X=3) - This means getting 3 heads in 4 coin tosses. There are 4 ways this can happen (H H H T, H H T H, H T H H, T H H H). So, P(X=3) = 4/16 = 1/4.
The probabilities for each outcome are:
P(X=0) = 1/16, P(X=1) = 1/4, P(X=2) = 3/8, P(X=3) = 1/4.