SOLUTION: The probabilities that two students will not show up for class on a beautiful spring day are 0.3 and 0.4, respectively. It is a beautiful spring day. Find the following probabiliti

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Question 1101497: The probabilities that two students will not show up for class on a beautiful spring day are 0.3 and 0.4, respectively. It is a beautiful spring day. Find the following probabilities. (See Example 6. Round your answers to two decimal places.)
(a) Neither will show up for class.

(b) Both will show up for class.

(c) Exactly one will show up for class.
Answer by greenestamps(13195) About Me  (Show Source):
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The given information is
P(A does not show up) = 0.3
P(B does not show up) = 0.4

We then know that
P(A shows up) = 1-0.3 = 0.7
P(B shows up) = 1-0.4 = 0.6

Then

(a) P(neither shows up) = P((A does not show up) AND (B does not show up)) = (0.3)(0.4) = 0.12
(b) P(both show up) = P((A shows up) AND (B shows up)) = (0.7)(0.6) = 0.42
(c) p(exactly one shows up) = P(((A shows up) AND (B does not)) OR ((B shows up) AND (A does not))) = (0.7)(0.4)+(0.6)(0.3) = 0.28 + 0.18 = 0.46

Note that the three cases together cover all the possibilities; so a good check of your answers is to show that the sum of the probabilities is 1:

0.12 + 0.42 + 0.46 = 1.00