If it rains tomorrow, the probability is 0.8 that john will practice the piano. if it does not rain tomorrow, there is only a. 4 chance that john will practice. if there is a 60% that it will rain tomorrow, what is the probability that John will practice his piano lesson? i'm supposed to use a tree diagram to solve this ... ?

P (J / R) = P (J and R) / P (R)

0.8 = P (J and R) / 0.6

P (J and R) = 0.6 * 0.8 = 0.48 [Probability John practicing and it is raining]

P (J / NR) = P (J and NR) / P (NR)

0.4 = P (J and NR) / (1 - 0.6) = P (J and NR) / 0.4

P (J and NR) = 0.4 * 0.4 = 0.16 [Probability John practicing and it is not raining]

Hence;

Propability of John practicing regardless of weather condition is

P (John Practicing) = 0.48 + 0.16 = 0.64