To solve this problem, we need to analyze the possible outcomes when two fair coins are tossed. Here is a detailed, step-by-step solution:
### Sample Space:
When two fair coins are tossed, the possible outcomes can be listed as follows:
1. Heads and Heads (HH)
2. Heads and Tails (HT)
3. Tails and Heads (TH)
4. Tails and Tails (TT)
So the complete sample space contains 4 outcomes: {HH, HT, TH, TT}.
### (a) Probability of Getting Two Tails (TT):
To find the probability of getting two tails, we look at how many of the outcomes involve getting two tails. From our sample space, only one outcome, TT, meets this criterion.
Number of favorable outcomes for two tails = 1
Total number of possible outcomes = 4
Therefore, the probability of getting two tails = Number of favorable outcomes / Total number of possible outcomes
[tex]\[ \text{Probability (Two Tails)} = \frac{1}{4} = 0.25 \][/tex]
### (b) Probability of Getting One Head and One Tail:
Next, we need to find the probability of getting one head and one tail. From our sample space, the outcomes HT and TH both satisfy this condition.
Number of favorable outcomes for one head and one tail = 2
Total number of possible outcomes = 4
Therefore, the probability of getting one head and one tail = Number of favorable outcomes / Total number of possible outcomes
[tex]\[ \text{Probability (One Head and One Tail)} = \frac{2}{4} = 0.5 \][/tex]
### Summary:
(a) The probability of getting two tails (TT) is [tex]\( 0.25 \)[/tex] or 25%.
(b) The probability of getting one head and one tail (HT or TH) is [tex]\( 0.5 \)[/tex] or 50%.
