if it can be assumed that 39.5% of all telephone #'s are unlisted, and that all telephone #'s are independent,find the probability that at least 1 of 5 telephone numbers are listed.
To find the probability that at least one of five telephone numbers is listed, we need to calculate the complement probability, which is the probability that none of the five numbers are listed, and then subtract it from 1.
Let's calculate the probability that a single telephone number is unlisted. Since 39.5% of all telephone numbers are unlisted, the probability that a single number is unlisted is 0.395.
Now, the probability that none of the five numbers are listed can be calculated by multiplying the probabilities of each number being unlisted:
P(None listed) = (0.395)^5
Finally, the probability that at least one of the five numbers is listed is:
P(At least one listed) = 1 - P(None listed)
P(At least one listed) = 1 - (0.395)^5
You can calculate this equation to find the exact probability that at least one of the five telephone numbers is listed.