3. For safety reasons, 5 different alarm systems were installed in the vault con

Question

3. For safety reasons, 5 different alarm systems were installed in the vault containing the safety deposit boxes at a Beverly Hills bank. Each of the 5 systems detects theft with a probability of 0.8 independently of the others. The bank, obviously, is interested in the probability that when a theft occurs, at least one of the 5 systems will detect it. What is the probability that when a theft occurs, at least one of the 5 systems will detect it? Your answer should be rounded to 5 decimal places.

4. In a certain liberal arts college with about 10,000 students, 44% are males. If two students from this college are selected at random, what is the probability that they are of the same gender? Your answer should be rounded to 4 decimal places.

5. According to the information that comes with a certain prescription drug, when taking this drug, there is a 18% chance of experiencing nausea (N) and a 44% chance of experiencing decreased sexual drive (D). The information also states that there is a 12% chance of experiencing both side effects. What is the probability of experiencing only nausea? Your answer should be to two decimal places.

6. According to the information that comes with a certain prescription drug, when taking this drug, there is a 19% chance of experiencing nausea (N) and a 52% chance of experiencing decreased sexual drive (D). The information also states that there is a 11% chance of experiencing both side effects. What is the probability of experiencing neither of the side effects? Your answer should be to two decimal places.

7. According to the information that comes with a certain prescription drug, when taking this drug, there is a 21% chance of experiencing nausea (N) and a 54% chance of experiencing decreased sexual drive (D). The information also states that there is a 13% chance of experiencing both side effects. What is the probability of experiencing nausea or a decrease in sexual drive? Your answer should be rounded to 2 decimal places.

8. An engineering school reports that 51% of its students are male (M), 39% of its students are between the ages of 18 and 20 (A), and that 28% are both male and between the ages of 18 and 20. What is the probability of a random student being chosen who is a female and is not between the ages of 18 and 20? Your answer should be to two decimal places.

Explanation / Answer

1)Given,

Probability of detecting a theft =0.8

For each single system of five, the probability that it will not detect a theft is . 1-0.8 = 0.2.

The probability that NO ONE of five systems will detect a theft is {{0.2^5}}} = 0.00032.

The probability that when a theft occurs, at least one of the 5 systems will detect it is =

1 - 0.00032 = 0.99968.

2) Probability of same gender =(0.44 *0.44) + (0.56 *0.56 ) =0.5072

3) 18 -12 =6

that is 6 percent =0.06 is th probability of experiencing only nausea

4)probability of experiencing both of the side effects =19+52 -11 =60 percent

probability of experiencing neither of the side effects =1-0.6 =0.4

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