Question

MC0402: Suppose there are two events, A and B.

The probability of event A is P(A) = 0.3.

The probability of event B is P(B) = 0.4.

The probability of event A and B (both occurring) is P(A and B) = 0.

Events A and B are:

	a.	40%
	b.	44%
	c.	56%
	d.	60%
	e.	None of these

a.

Complementary events

b.

The entire sample space

c.

Independent events

d.

Mutually exclusive events

e.

None of these

MC0802: Functional Robotics Corporation buys electrical controllers from a Japanese supplier. The Company's treasurer feels that there is a probaility of 40% that the dollar will fall in value against the Japanese Yen in the next month. The treasurer also believes that if the dollar falls, there is an 80% probability that the supplier will demand renegotiation of the contract. If the dollar does not fall, the treasurer believes that there is a 20% probability that the supplier will demand renegotiation. What is the probability that the supplier will demand renegotiation?

MC1102: Suppose that 2% of a clinic's patients are known to have cancer. A blood test is developed that is positive (gives a cancer diagnosis) in 98% of the patients with cancer but is also positive in 3% of patients who do not have cancer. If a person is chosen at random from the clinic's patients is given the test and it comes out positive, what is the probability that the person actually has cancer? You might want to construct a table or tree-diagram to answer this.

a.

0.02

b.

0.4

c.

0.5

d.

0.6

e.

0.98

f.

None of these

MC1202: You can choose one of three boxes. Box A has four $5 bills and one $100 bill. Box B has 400 $5 bills and 100 $100 bills. Box C has 24 $1 bills. You can take all of Box C, or blindly pick one bill out of either Box A or Box B. Which offers the greatest expected winning?

	a.	Box A
	b.	Box B
	c.	Box C
	d.	Either Box A or Box B, but not Box C
	e.	All three offer the same expected winning.

Answer 1

MC0402: Events A and B are: Mutually exclusive events ; option D

MC0802:  probability that the supplier will demand renegotiation =P(Dollar falls and  renegotiation+not falls and  renegotiation)=0.4*0.8+(1-0.4)*0.2=0.44

MC1102: P(Cancer|test positive)=P(Cancer and test positive)/P(test positive)

=0.02*0.98/(0.02*0.98+0.98*0.03)=0.4 ; option B

MC1202

expected value of box A =(4*5+100)/5=24

expected value of box B =(400*5+100*100)/500=24

expected value of box C =24*1=24

option E is correct All three offer the same expected winning.