Question

1. when unusual event. matching probabilities in exercises 11–16, match the event with probability. (a) 0.95 (b) 0.005 (c) 0.25 (d) 0 (e) 0.375 (f) 0.5 11. a random number generator is used to select a number from 1 to 100. what is the probability of selecting the number 153? 12. a random number generator is used to select a number from 1 to 100. what is the probability of selecting an even number? 13. you randomly select a number from 0 to 9 and then randomly select a number from 0 to 19. what is the probability of selecting a 3 both times? 14. a game show contestant must randomly select a door. one door doubles her money while the other three doors leave her with no winnings. what is the probability she selects the door that doubles her money? 15. five of the 100 digital video recorders (dvrs) in an inventory are known to be defective. what is the probability you randomly select a dvr that is defective? 16. you toss a coin four times. what is the probability of tossing tails exactly of the time?

Explanation:

Step1: Q11: Define possible outcomes

Total numbers: 1-100, so 100 valid outcomes. 153 is not in this range, so 0 favorable outcomes.
Probability: $\frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{0}{100} = 0$

Step2: Q12: Count even numbers 1-100

Even numbers: 2,4,...,100. There are $\frac{100}{2}=50$ even numbers.
Probability: $\frac{50}{100} = 0.5$

Step3: Q13: Calculate independent probabilities

Probability of 3 from 0-9: $\frac{1}{10}$. Probability of 3 from 0-19: $\frac{1}{20}$.
Combined probability: $\frac{1}{10} \times \frac{1}{20} = 0.005$

Step4: Q14: Count winning doors

1 winning door, 4 total doors.
Probability: $\frac{1}{4} = 0.25$

Step5: Q15: Count defective DVRs

5 defective DVRs, 100 total DVRs.
Probability: $\frac{5}{100} = 0.05$ (Note: 0.05 is not listed, but correction: $\frac{5}{100}=0.05$, but if matching given options, no match? Wait, correction: 5/100=0.05, but closest? No, recheck: 5 defective out of 100 is 0.05, but if we misread? No, 5/100=0.05. Wait, maybe typo? No, proceed.

Step6: Q16: Use binomial probability

Toss 4 times, exactly 2 tails. Number of ways: $\binom{4}{2}=6$. Total outcomes: $2^4=16$.
Probability: $\frac{6}{16} = 0.375$

Answer:

1. 0 (matches option d)
2. 0.5 (matches option f)
3. 0.005 (matches option b)
4. 0.25 (matches option c)
5. 0.05 (no listed match; correction: $\frac{5}{100}=0.05$)
6. 0.375 (matches option e)