Question

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 ...?

Answer 1

Answer:64 %

Explanation:

Given if it rains John Plays piano is 0.8

i.e. if it rains probability that john will not play is 0.2

If it not rain Then probability that john will play piano is 0.4

he will not play is 0.6

Given if there is 60 % chance that it will rain tomorrow

Thus Pobability that john will play is

`=Probability\ that\ it\ will * Probability\ john\ will\ play+Probability\ it\ will\ not\ rain* Probability john will play`

`=0.6* 0.8+0.4* 0.4=0.48+0.16=0.64`

Answer 2

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