1. **Problem Statement:** We need to formulate a probability mass function (PMF) for the number of days Ingrid takes the yellow bus to school over three consecutive days. 2. **Understanding the PMF:** A PMF gives the probability that a discrete random variable takes a specific value. Here, the random variable $X$ is the number of days Ingrid takes the yellow bus in 3 days. 3. **Assumptions:** Assume the probability Ingrid takes the yellow bus on any given day is $p$, and the days are independent. 4. **Formula:** The PMF for $X$ (a binomial distribution) is: $$P(X = k) = \binom{3}{k} p^k (1-p)^{3-k}$$ where $k = 0,1,2,3$. 5. **Explanation:** - $\binom{3}{k}$ counts the ways to choose $k$ days out of 3. - $p^k$ is the probability she takes the bus on those $k$ days. - $(1-p)^{3-k}$ is the probability she does not take the bus on the other days. 6. **Example:** If $p=0.6$, then the probability she takes the bus exactly 2 days is: $$P(X=2) = \binom{3}{2} (0.6)^2 (0.4)^1 = 3 \times 0.36 \times 0.4 = 0.432$$ This PMF fully represents the distribution of the number of days Ingrid takes the yellow bus over three days.