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23 Apr 2018, 23:52
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Katie, Ace, and Rory interviewed for jobs at companies A, B, and C, respectively. The probability that Katie will get a job offer from company A is 1/4 ; the probability that Ace will get a job offer from company B is 1/2; and the probability that Rory will get a job offer from company C is 5/8 . The three companies have no connections to one another, so the job offers are mutually independent. What is the probability that Katie and Ace will get job offers, but not Rory?
(A) 3/64
(B) 5/64
(C) 18
(D) 3/8
(E) 9/8
(A) 3/64
(B) 5/64
(C) 18
(D) 3/8
(E) 9/8
24 Apr 2018, 00:43
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Bunuel
Katie, Ace, and Rory interviewed for jobs at companies A, B, and C, respectively. The probability that Katie will get a job offer from company A is 1/4 ; the probability that Ace will get a job offer from company B is 1/2; and the probability that Rory will get a job offer from company C is 5/8 . The three companies have no connections to one another, so the job offers are mutually independent. What is the probability that Katie and Ace will get job offers, but not Rory?
(A) 3/64
(B) 5/64
(C) 18
(D) 3/8
(E) 9/8
(A) 3/64
(B) 5/64
(C) 18
(D) 3/8
(E) 9/8
As this is a very long word question, we'll first write down what we're told as expressions so we don't get confused.
This is a Precise approach.
Katie, company A: p = 1/4
Ace, company B: p = 1/2
Rory, company C: p = 5/8
question: Katie and Ace get job offer, Rory doesn't.
Now that everything is nice and organized, it should be clear that our calculation is 1/4 * 1/2 * (1 - 5/8) = 1/8 * 3/8 = 3/64.
(A) is our answer.
11 Dec 2019, 23:23
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Let us use variables to represent the different probabilities.
Let K represent the probability that Katie will get a job offer. Given that K = \(\frac{1}{4}\). Therefore, K’ represents the probability that Katie won’t get the job offer. Since these are mutually exclusive, K + K’ = 1. This gives us K’ = \(\frac{3}{4}\).
Similarly, we can calculate A’ = ½ given A = ½ and R’ = \(\frac{3}{8}\) given R = \(\frac{5}{8}\).
Now, the event for which we are trying to find the probability is that Katie and Ace should get job offers while Rory should not. This means, all the three have to happen at the same time, which means we will have to multiply the respective probabilities.
Therefore, required probability = K * A * R’ =¼ * ½ * \(\frac{3}{8}\) = \(\frac{3}{64}\).
The correct answer option is A.
Hope that helps!
Let K represent the probability that Katie will get a job offer. Given that K = \(\frac{1}{4}\). Therefore, K’ represents the probability that Katie won’t get the job offer. Since these are mutually exclusive, K + K’ = 1. This gives us K’ = \(\frac{3}{4}\).
Similarly, we can calculate A’ = ½ given A = ½ and R’ = \(\frac{3}{8}\) given R = \(\frac{5}{8}\).
Now, the event for which we are trying to find the probability is that Katie and Ace should get job offers while Rory should not. This means, all the three have to happen at the same time, which means we will have to multiply the respective probabilities.
Therefore, required probability = K * A * R’ =¼ * ½ * \(\frac{3}{8}\) = \(\frac{3}{64}\).
The correct answer option is A.
Hope that helps!
