Answer:
In the experiment where three fair coins are tossed simultaneously, the sample space consists of all possible outcomes of the three coin tosses. Each coin can land heads (H) or tails (T), so there are 2^3 = 8 possible outcomes:
1. HHH
2. HHT
3. HTH
4. HTT
5. THH
6. THT
7. TTH
8. TTT
Now, let's denote N as the number of tails obtained from this experiment. N can take on values from 0 to 3, as there can be 0, 1, 2, or 3 tails in the three coin tosses. We can find the probabilities associated with each value of N as follows:
1. N = 0 (No tails): There is only one outcome with no tails, which is HHH.
P(N = 0) = 1/8
2. N = 1 (One tail): There are three outcomes with one tail: HHT, HTH, and THH.
P(N = 1) = 3/8
3. N = 2 (Two tails): There are three outcomes with two tails: HTT, THT, and TTH.
P(N = 2) = 3/8
4. N = 3 (Three tails): There is only one outcome with three tails, which is TTT.
P(N = 3) = 1/8
So, the probability distribution for N, the number of tails obtained, is as follows:
P(N = 0) = 1/8
P(N = 1) = 3/8
P(N = 2) = 3/8
P(N = 3) = 1/8
These probabilities represent the likelihood of obtaining each possible number of tails when three fair coins are tossed simultaneously.
Explanation: