a computers random number generator produces random integers from 1 to 50. what is the probability that at…

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?\n0.0016\n0.1024\n0.4096\n0.5904

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?\n0.0016\n0.1024\n0.4096\n0.5904

Answer

Explanation:

Step1: Calculate non - 20s probability

The numbers from 1 to 50, there are 10 numbers in the 20s (20 - 29). So there are 50 - 10 = 40 non - 20s numbers. The probability that a single generated number is not in the 20s is $p=\frac{40}{50}=0.8$.

Step2: Calculate probability of no 20s in 4 numbers

Since the generation of each number is an independent event, the probability that none of the first 4 generated numbers is in the 20s is $P(\text{none})=(0.8)^4 = 0.4096$.

Step3: Calculate probability of at least one 20s

The probability that at least one of the first 4 generated numbers is in the 20s is the complement of the event that none of them is in the 20s. So $P(\text{at least one}) = 1 - P(\text{none})=1 - 0.4096=0.5904$.

Answer:

0.5904