Question

Question 2

Two cards are drawn without replacement from a well-shuffled deck of 52 playing cards. What is the probability that the first card drawn is a 6 and the second card drawn is a 7?

a) 0.0059

b) 0.0045

c) 0.0060

d) 0.1569

e) 0.1554

Question 6

John is interested in purchasing a multi-office building containing five offices. The current owner provides the following probability distribution indicating the probability that the given number of offices will be leased each year.

Number of Lease Offices	0	1	2	3	4	5
Probability	5/28	1/4	1/7	2/7	1/28	3/28

If each yearly lease is $12,000, how much could John expect to collect in yearly leases for the whole building in a given year?(in dollars)

a) E(X) = $24,797.14

b) E(X) = $24,887.14

c) E(X) = $24,777.14

d) E(X) = $24,787.14

e) E(X) = $24,857.14

Answer 1

2 ) no. of 6 numbered cards = 4

no. of 7 numbered cards = 4

The probability that the first card drawn is a 6 and the second card drawn is a 7 is,

= (4C1*4C1)/(52C1*51C1)

= 16/2652

= 0.0060 (option - C)

6) from the given data,

Expected value = $\sum$ X*P(X) = 0*5/28 + 1*1/4 + 2*1/7 + 3*2/7 + 4*1/28 + 5*3/28 = 2.071428571

Expected amount, E(X) = 2.071428571*12000 = $24857.14 (option - e)