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23 June, 02:44

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 ... ?

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  1. 23 June, 03:05
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    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
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