1. **Problem Statement:** We have 3 coin tosses with outcomes either W (Worn attack) or N (None). We want to analyze the random variable $X$ which counts the number of tails (W) in each outcome. 2. **Possible Outcomes:** There are $2^3=8$ possible outcomes for 3 coin tosses: NNN, NNW, NWN, WNN, WWN, WNW, NWW, WWW. 3. **Random Variable $X$ Definition:** $X$ counts the number of tails (W) in each outcome. 4. **Outcome Values:** - $X=0$ for NNN - $X=1$ for NNW, NWN, WNN - $X=2$ for WWN, WNW, NWW - $X=3$ for WWW 5. **Probability Distribution:** Since each outcome is equally likely with probability $\frac{1}{8}$, the probabilities for $X$ are: $$ P(X=0) = \frac{1}{8},\quad P(X=1) = \frac{3}{8},\quad P(X=2) = \frac{3}{8},\quad P(X=3) = \frac{1}{8} $$ 6. **Explanation:** The distribution is binomial with parameters $n=3$ and $p=\frac{1}{2}$ (probability of tail per toss). The probabilities match the binomial formula: $$ P(X=k) = \binom{3}{k} \left(\frac{1}{2}\right)^k \left(\frac{1}{2}\right)^{3-k} = \binom{3}{k} \frac{1}{8} $$ for $k=0,1,2,3$. 7. **Summary:** The random variable $X$ representing the number of tails in 3 coin tosses has the probability distribution: | Tails ($X$) | Probability $P(X)$ | |-------------|-------------------| | 0 | $\frac{1}{8}$ | | 1 | $\frac{3}{8}$ | | 2 | $\frac{3}{8}$ | | 3 | $\frac{1}{8}$ | This matches the given data and the binomial distribution for 3 tosses with fair coins.