1. A Student has applied for a job with two companies: X and Y. The graduate fee

Question

1. A Student has applied for a job with two companies: X and Y. The graduate feels that she has a 60% chance of receiving an offer from Company X and a 40% chance of receiving an offer from company Y. If she receives an offer from Company Y, she believes that she has an 70% chance of receiving an offer from Company X. a) What is the probability that both companies will make her an offer? b) What is the probability that at least one company will make her an offer? 2. The number of burgers (X) delivered to QU students each week has the following probability distribution: X P(x) .3 .4 .2 3 If the burger shop makes a profit of 5 QR per burger, what is the mean and standard deviation of the profit per week? 3, A survey found that 40% of the students think that the Business Statistics course needs to be more challenging. If 25 of the students are randomly chosen, what is the probability that at least 11 of them would agree that Business Statistics course needs to be more challenging?

Explanation / Answer

Question 1:

Here we are given that: P(X) = 0.6, P(Y) = 0.4 and also given Y , 70% chance of getting from X which means that:

P(X | Y) = 0.7

a) Using bayes theorem, we get:

P(X and Y) = P(X | Y)P(Y) = 0.7*0.4 = 0.28

Therefore 0.28 is the required probability that both the companies will offer him .

b) Probability that at least one will make an offer is computed using law of addition of probability as:

P( X or Y) = P(X) + P(Y) - P(X and Y) = 0.6 + 0.4 - 0.28 = 0.72

Therefore 0.72 is the required probability here.

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