A customer service division of a telecommunications firm

receives 100 mobile phones for repair on a particular week. 18 of
the phones are less than a year, 60 phones are more than a
year but less than 2 years and the rest are older than 2 years.
The company provides warranty for phones less than a year old.
Compute the probability that a phone chosen at random will
meet the following criteria:
a. Under warranty period
b. Older than 2 years
c. Less a year old or more than 2 years old
d. Not covered under warranty

To compute the probabilities, we need to calculate the number of phones that meet each criteria and divide by the total number of phones.

a. Under warranty period:
The number of phones that are less than a year old is given as 18.
So, the probability that a phone chosen at random is under warranty is 18/100.

b. Older than 2 years:
The number of phones that are older than 2 years is not provided explicitly in the question. However, we can calculate it by subtracting the number of phones less than a year old and the number of phones between 1 and 2 years from the total number of phones.
Number of phones older than 2 years = Total number of phones - Number of phones less than a year old - Number of phones between 1 and 2 years
Number of phones older than 2 years = 100 - 18 - 60
Number of phones older than 2 years = 22
So, the probability that a phone chosen at random is older than 2 years is 22/100.

c. Less than a year old or more than 2 years old:
To calculate this probability, we need to consider the phones that are either less than a year old or older than 2 years. The number of phones that are less than a year old is given as 18, and the number of phones older than 2 years is calculated as 22.
Number of phones less than a year old or older than 2 years = Number of phones less than a year old + Number of phones older than 2 years
Number of phones less than a year old or older than 2 years = 18 + 22 = 40
So, the probability that a phone chosen at random is less than a year old or older than 2 years is 40/100 = 2/5.

d. Not covered under warranty:
The question asks for the probability that a phone chosen at random is not covered under warranty. This means the phone should be older than a year.
To calculate this probability, we need to consider the phones that are older than a year. The number of phones older than a year is given as 60.
So, the probability that a phone chosen at random is not covered under warranty is 60/100 = 3/5.

To compute the probability, we need to determine the number of phones that meet each criteria and then divide by the total number of phones.

a. To find out the number of phones under warranty, we know that 18 phones are less than a year old. So the probability of a phone being under warranty is 18/100 = 0.18.

b. We're given that the remaining phones that are older than 2 years are not covered under warranty. So the probability of a phone being older than 2 years and not under warranty is the number of phones older than 2 years divided by the total number of phones. Since we know 60 phones are between 1 and 2 years old, the remaining phones must be older than 2 years. Therefore, the probability is (100 - 18 - 60)/100 = 0.22.

c. To calculate the probability of a phone being less than a year old or more than 2 years old, we can add the probabilities of a and b, and subtract it from 1 (since the sum of all probabilities should be equal to 1). So the probability is 1 - (0.18 + 0.22) = 0.6.

d. Lastly, to determine the probability of a phone not being covered under warranty, we can subtract the probability of a from 1. So the probability is 1 - 0.18 = 0.82.

In summary:
a. Probability of a phone being under warranty = 0.18
b. Probability of a phone being older than 2 years and not under warranty = 0.22
c. Probability of a phone being less than a year old or more than 2 years old = 0.6
d. Probability of a phone not covered under warranty = 0.82