suppose you just received a shipment of 13 tvs. 3 of them are defective. if 2 tvs are randomly selected compute the probability that both tvs work and what is the probability at least one doesn't work? answer as a fraction in simplified form
To compute the probability that both TVs work, we need to determine the number of favorable outcomes (both working TVs) divided by the total number of possible outcomes (two randomly selected TVs).
There are 13 TVs in total, out of which 3 TVs are defective. So, there are 13 - 3 = 10 working TVs.
The probability of selecting a working TV on the first pick is 10/13, and since we do not replace the first TV, the probability of selecting another working TV on the second pick is 9/12 (as there are now 12 remaining TVs, with 9 working TVs).
To calculate the probability of both TVs working, we multiply the individual probabilities:
Probability of both TVs working = (10/13) * (9/12) = 90/156 = 15/26
To find the probability that at least one doesn't work, we can use the complement rule. The complement of "at least one doesn't work" is "both TVs work." We already know the probability of both TVs working is 15/26, so the probability of at least one doesn't work is:
Probability of at least one doesn't work = 1 - Probability of both TVs working
= 1 - 15/26
= (26/26) - (15/26)
= 11/26
Therefore, the probability that both TVs work is 15/26, and the probability that at least one doesn't work is 11/26.
To compute the probability that both TVs work, we need to calculate the probability of selecting a working TV on the first pick and then, given that the first TV was working, selecting another working TV on the second pick.
First, let's calculate the probability that the first TV selected works. Out of the 13 TVs, 3 are defective, so there are 13 - 3 = 10 working TVs.
Therefore, the probability of selecting a working TV on the first pick is 10/13.
Now, to find the probability of selecting another working TV given that the first TV was working, we need to consider the second pick. After selecting one working TV, there are now 9 working TVs left out of the remaining 12 TVs.
Therefore, the probability of selecting a second working TV is 9/12.
To find the probability that both TVs work, we multiply the two probabilities together:
(10/13) * (9/12) = 90/156 = 15/26.
So, the probability that both TVs work is 15/26.
Now, to find the probability that at least one TV doesn't work, we can use the complement rule. The complement of "at least one TV doesn't work" is "both TVs work."
Therefore, the probability that at least one TV doesn't work is 1 - (15/26) = 11/26.
So, the probability that at least one TV doesn't work is 11/26.