Question

3) (15 pts total) Sampling without replacement
A box in the EE188 lab contains 200 resistors that are labeled 100k? resistors. Five of these resistors are in fact 10 k? resistors (only 5!) Your circuit design uses 3 100 k? resistors.

a) (5 pts) What is the probability that all 3 of the resistors you choose are 100k? resistors?

b) (5 pts) What is the probability that one or more or the 3 resistors that you chose aren’t 100

k? resistors? Hint: use the answer from part a)

c) (5 pts) What is the probability that all 3 resistors that you chose are not 100 k? resistors.

Answer 1

ANSWER:

Total number of resistors in the box is 200+20=220

Total number of ways of selecting 3 resistors out of 220 is C(220, 3)

(a)

Number of ways of selecting 3 resistors out of 200 resistors is C(200,3)

So the requried probability is C(200,3) / C(220,3)= 0.7503

(b)

Here we need to find the probability that at least one resistor is not of 100k. By the cmplement rule we have

1 - 0.7503 = 0.2497

(c)

Number of ways of selecting 3 resistors out of 20 is C(20,3).

So the requried probability is C(20.3) / C(220,3) = 0.00065