1) From the sample space S = (1,2,3,4,......,15), a single number is to be selected at random. Given the following events, find the indicated probability. A) The selected number is even B) The selected number is a multiple of 4 C) The selected number is a prime number

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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1) From the sample space S = (1,2,3,4,......,15), a single number is to be selected at random. Given the following events, find the indicated probability. 
A) The selected number is even

B) The selected number is a multiple of 4 

C) The selected number is a prime number 

P (B and C) 

2) Six men and four women are waiting to be interviewed for jobs. If they are all selected in random order, find the probability that no man will be interviewed until at least two women have been interviewed. 

3) In November, the rain in a certain valley tends to fall in storms on several days' duration. The unconditional probability of rain on any given day of the month is 0.700. But the probability of rain on a day that follows a rainy day is 0.800, and the probability of rain on a day following a nonrainy day is 0.400. Find the probability of rain on November 1 and 2, but not on November 3. 

4) A person is taking a 12-question multiple-choice test for which each question has three answer choices, only one of which is correct. The person decides on answers by rolling a fair die and marking the first answer choice if the die shows 1 or 2, the second if it shows 3 or 4, and the third if it shows 5 or 6. Find the probability that the person gets fewer than 3 correct answers.

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