Question

Draw an appropriate tree diagram, and use the multiplication principle to calculate the probabilities of all the outcomes. HINT [See Example 3.]

There is a 60% chance of rain today and a 40% chance of rain tomorrow. Assume that the event that it rains today is independent of the event that it rains tomorrow. What is the probability that it rains on exactly one of the next two days?

Answer 1

P (Rain Today) = 0.6 => P(It does not rain today) = 0.4

P (Rain Tomorrow) = 0.4 => P(It does not rain tomorrow) = 0.6

Let us take that,

? means it rains

X means it does not rain

The possibilities are- ?X and X?

So, for each case, the probabilities are as follows-

?X : 0.6*0.6 = 0.36

X? : 0.4*0.4 = 0.16

So, total probability that it rains exactly on one day = 0.36+0.16 = 0.52

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