Question

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Math 180A: Sample Midterm Exam 1 1. Suppose there is 50 percent chance that it rains on Monday, and 60 percent chance that it rains ou Tueday. Suppose there is 40 pnt chhauce hat raob (a) What is the probability that it rains on Monday, but not on Tuesday? (b) What is the probability that there is no rain on either day? (c) Is "rain on Monday" independent of "rain in Tuesday"? Why? n days.

Answer 1

1. P(rain of Monday) = 0.5

P(rain on Tuesday) = 0.6

P(Rain on Monday and Tuesday) = 0.4

a) P(it rain of Monday, but not on Tuesday) = P(It rains on Monday) - P(It rains on Monday and Tuesday)

= 0.5 - 0.4

= 0.1

b) P(A or B) = P(A) + P(B) - P(A & B)

P(rain on Monday or Tuesday) = P(rain on Monday) + P(rain on Tuesday) - P(rain on Monday and Tuesday)

= 0.5 + 0.6 - 0.4

= 0.70

P(no rain on either day) = 1 - P(rain on Monday or Tuesday)

= 1 - 0.70

= 0.30

c) Two events A and B are independent if P(A) x P(B) = P(A & B)

P(rain on Monday) x P(rain on Tuesday) = 0.5 x 0.6 = 0.3

P(rain on Monday and Tuesday) = 0.4

P(rain on Monday) x P(rain on Tuesday) $\small \neq$ P(rain on Monday and Tuesday)

So, the events are not independent