The probability of snow tomorrow is \( \frac{3}{5} \). If it snows tomorrow, the probability that John will practice his guitar is \( \frac{7}{10} \). If it does not snow tomorrow, the probability that John will practice his guitar is \( \frac{1}{2} \). What is the probability that John will practice his guitar tomorrow? \( P(J o h n \) will practice) \( =\square \) (Type an integer or a simplified fraction.)

To find the probability that John will practice his guitar tomorrow, we can use the law of total probability. Let \( S \) be the event that it snows tomorrow, and \( P \) be the event that John practices his guitar. We know: - \( P(S) = \frac{3}{5} \) (Probability of snow) - \( P(P | S) = \frac{7}{10} \) (Probability John practices if it snows) - \( P(\neg S) = 1 - P(S) = \frac{2}{5} \) (Probability it does not snow) - \( P(P | \neg S) = \frac{1}{2} \) (Probability John practices if it does not snow) Now we can calculate the total probability that John practices his guitar: \[ P(P) = P(P | S) \cdot P(S) + P(P | \neg S) \cdot P(\neg S) \] Substituting in the values: \[ P(P) = \left(\frac{7}{10} \cdot \frac{3}{5}\right) + \left(\frac{1}{2} \cdot \frac{2}{5}\right) \] Calculating each term: 1. \( \frac{7}{10} \cdot \frac{3}{5} = \frac{21}{50} \) 2. \( \frac{1}{2} \cdot \frac{2}{5} = \frac{1}{5} = \frac{10}{50} \) Now, adding these probabilities together: \[ P(P) = \frac{21}{50} + \frac{10}{50} = \frac{31}{50} \] Thus, the probability that John will practice his guitar tomorrow is \( \frac{31}{50} \). So, \( P(J o h n \) will practice) \( = \frac{31}{50} \)