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151midterm1sol

# First Course in Probability, A (7th Edition)

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Math 151 Midterm 1 Solutions 1. Suppose that 28 percent of the population drink tea, 35 percent drink coffee, 10 percent drink both. Find: ( i ) percentage of people who do not drink either. ( ii ) percentage of people who drink tea but not coffee Solution. (i) Answer: 47 percent (ii) Answer: 18 percent 2. Show that if events A, B, C are independent, then so are A and B C Solution. P ( A ( B C ) = P ( AB AC ) = P ( AB ) + P ( AC ) - P ( ABC ) = P ( A ) P ( B ) + P ( A ) P ( C ) - P ( A ) P ( B ) P ( C ) = P ( A )[ P ( B ) + P ( C ) - P ( BC )] = P ( A ) P ( B C ) In above steps we used independence between A, B and C and proposition from textbook. 3. Two hunters shoot at a deer, which is hit by exactly one bullet. If the first hunter hits targets with probability 0.3 and the second with probability 0.6, what is the probability the second hunter killed the deer? The answer is not 2/3. Solution. Let D =”Deer is hit by exactly one bullet”, F =”The first hunter killed the deer”, S =”The second hunter killed the deer” P ( S | D ) = P ( SD ) P ( D ) = P ( S ) P ( D | S ) P ( S ) P ( D | S )+ P ( F ) P ( D | F ) = (0 . 6)(0 . 7) (0 . 6)(0 . 7)+(0 . 3)(0 . 4) = 0 . 42 0 . 54 = 7 9 4.

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151midterm1sol - Math 151 Midterm 1 Solutions 1 Suppose...

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