ZEXT ONLYYY

NEEDED IN 3 HRS

1. Mr. Smith applies for a bank loan. The probability that it will be approved is 2/3. If the
loan is approved, the probability that his business venture will succeed is ¾. However if
the loan is not approved, the probability that his business venture will succeed is only
¼.

a) What is Mr. Smith’s probability od success in his business venture?
b) Given that Mr. Smith’s business venture failed, what is the probability that he

did not obtain a bank loan?

2. Snow White is scrubbing the kitchen floor when the doorbell rings. The Wicked
Queen, disguised as an old woman, offers her a basket containing 5 apples, of which 1 is
poisonous, 2 are wormy, and 2 are good. Snow White picks up the apples randomly one
by one and eats them. Assume that:
i) If she bites the poisonous apple, she dies instantly;
ii) If she bites a wormy apple, she gives the rest of that apple to the pig;
iii) If the pig eat a wormy apple, he dies right away (!)
Compute the probability that:
a)the pig dies; b)Snow White eats all the good apples

3. Suppose a box contains 4 balls numbered 1, 2, 3, 4.Two balls are randomly drawn w/o
replacement.Let X denote the larger of the two numbers on the balls selected.
Find the pdff(x) and the cdf F(x). Find E (x).

4.

a) If a continuous random variable X has p.d.f. f (x) as shown on the picture what
should be the value of h?

b) Compute P (1< x≤ 2) and P (x ≥ 2) 5. A carton of eggs has 3 bad eggs and 9 good eggs. If an omelette is made of 3 eggs randomly selected from the carton, a) what is the probability of having at least one bad egg in the omelette? b )what is the probability of having exactly 2 bad eggs in the omelette? c)compute E(x^2)-[E(x)]^2