2. A recreational equiprnent supplier finds that among orders that include tents
ID: 3320013 • Letter: 2
Question
2. A recreational equiprnent supplier finds that among orders that include tents, 40% also include sleeping mats. Only 5% of orders that do not include tents do include sleeping mats. Also, 20% of orders include tents. Determine the following probabilities (a) The order includes sleeping mats? (1 point) (b) The order includes a tent given it includes sleeping mats. (1 point) (c) The order includes a tent and a sleeping pad? (1 point) (d) The order does not include a sleeping pad given it includes tents? (1.5 point) (e) The order does not include a sleeping pad given it does not include tents? (1.5 point)Explanation / Answer
Let A denote the order of sleeping mats and B include the order of tents.
P(A|B) = 0.4 P(A|B') = 0.05 P(B) = 0.2
P(B') = 1 - 0.2 = 0.8
(c) P(A and B) = P(A|B) P(B) = 0.4 * 0.2 = 0.08.
(a) P(A and B') = P(A|B') P(B') = 0.05 * 0.8 = 0.04.
P(A) = P(A and B) + P(A and B') = 0.08 + 0.04 = 0.12.
(b) P(B|A) = P(A and B) / P(A) = 0.08 / 0.12 = 0.6667.
(d) P(A' and B) = P(B) - P(A and B)
= 0.2 - 0.08 = 0.12.
P(A'|B) = P(A' and B) / P(B)
= 0.12 / 0.2 = 0.6.
(e) P(A' and B') = P(B') - P(A and B')
= 0.8 - 0.04
= 0.76
P(A'|B') = P(A' and B') / P(B')
= 0.76 / 0.8
= 0.95.
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