Question

a computers random number generator produces random integers from 1 to 50. what is the probability that at least one of the first 4 generated numbers is in the 20s?
0.0016
0.1024
0.4096
0.5904

Explanation:

Step1: Calculate the probability of a single number not being in the 20s

There are 10 numbers in the 20s (20 - 29). So the number of non - 20s numbers is \(50−10 = 40\). The probability that a single number is not in the 20s is \(p=\frac{40}{50}=0.8\).

Step2: Calculate the probability that none of the 4 numbers is in the 20s

Since the numbers are generated independently, we use the multiplication rule for independent events. The probability that none of the 4 numbers is in the 20s is \(P(\text{none})=(0.8)^4\).

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Step3: Calculate the probability that at least one number is in the 20s

We use the formula \(P(\text{at least one})=1 - P(\text{none})\).

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Answer:

0.5904