TEORI PROBABILITAS IE 1323

SOEWONO, DRS

EXERCISES1.) Bag A has three red balls and two white balls, and bag B has two red balls and five white balls.

A fair coin is tossed. if it lands heads up, a ball is drawn from bag A; otherwise, a ball is drawn from bag B.

a. what is the probability that a red ball is drawn? b. if a red ball is drawn, what is the probability that the coin landed heads up?

2.) Two bags B1 and B2 contain, respectively, three white and five black balls, and four white and six black balls. One ball is drawn from B1 and placed in B2. Then a ball is drawn from B2 and turns out to be black. What is the probability that the ball drawn from B1 was white?

3.) In a bolt factory, machines A, B and C manufacture 25, 35 and 40 percent of the total output, respectively. Of their outputs, 5, 4 and 2 percent, respectively, are defective bolts. A bolt is chosen at random and found to be defective. what is the probability that the bolt came from machine A, B and C?

4.) An assembler of electric fans uses motors from two sources. Company A supplies 90% of the motors and company B supplies the other 10% of the motors. Suppose it is known that 5% of the motors supplied by company A are defective and 3% of the motors supplied by company B defective. An assembled fan is found to have a defective motor. what is the probability that this motor was supplied by company B?

5.) let P(A)= 0,4 and P(AUB) = 0,7. what is P(B) if : a. A B b. A B

6.) let P(AUB) = 0,75 and P(A ∩ B) = 0.25. Is it possible to determine P(A) and P(B) Answer the same question if, in addition: a. A B b. A B

7.) the events A and B are mutually exclusive. Determine which of the following relations are true and which are false. a. P(AIB) = P(A) b. P(AUB I C) = P(AIC) + P(BIC) c. P(A∩B) = P(A).P(B)

Repeat the above if the events A and B are independent.

8. In three boxes there are capacitors as shown in table

(below). An experiment consists of first randomly

selecting a box, assuming each has the same

likelihood of selection, and then selecting a capacitor

from choosen box.

Value (µF)Number in boxTotals

123

0.01209525140

0.10553575165

1.007080145295

Totals145210245600

a.) What is the probability of selecting a 0.01 µF capacitor, given that box 2 is selected?

b.) If a 0.01 µF capacitor is selected,

what is the probability it came from

box 3?

9. In the switching in figure (below), the switches S1, S2, S3 and S4 are open or closed at random and

independently. The probability that any switch is

closed at a given time equals p. What is at least one

closed path form L to R?

LS4

S3

S2S1

R

10. In figure (a) and (b) assume that the

probability of each switches being closed is p

and that each switches is open or closed

indepedently.Find the probability that current flows from L to R?

L

S3S4

S5

S2S1

R

L

S6S5

S4R

S2

S3

S1

(a)

11. A box contains seven red and 13 blue balls. Two balls are selected at random and are discarded without their colours being seen.

if a third ball is drawn randomly and observed to be red, what is the probability that both of the discarded balls were blue?

12. Let A and B be two events associated with RE. Suppose that P(A)=0.4 while P(AUB)=0.7. Let P(B)=p. For what choice p are A and B(a). Mutually Exclusive Events(b). Independent Events