- #1
r0bHadz
- 194
- 17
Homework Statement
Out of six computer chips, two are defective. If two chips are randomly chosen for testing
(without replacement), compute the probability that both of them are defective. List all
the outcomes in the sample space.
Homework Equations
The Attempt at a Solution
I want to know:
P(both draws are defective)
= P(draw one is defective and draw 2 is defective)
= P(draw one is defective ∩ draw 2 is defective)
I'm confused. intuitively 2/6 * 1/5 makes sense to me and this is indeed the answer. But I am trying to understand the subject in terms of definitions and formulas, and I end up getting lost..
I have "events e1,e2,...en are independent if they occur independently of each other, occurence of one events does not effect the probability of another"
well (1/5)(2/6) is the probability of a intersect of independent events. But I don't see how they could possibly be independent. If we said "with replacement" I could see the case being made, but the question says without replacement, so the probability of getting a defective chip on the first draw effects the probability of getting a defective chip on the second draw.
I have "events A and B are disjoint if A∩B= ∅ " and under my current definition of the outcomes for this set, they are not disjoint either, so they cannot be mutually exclusive. That leaves me with no formulas I can work with.
Maybe changing the outcomes from: {a defective chip is drawn, a non defective chip is drawn}
to
{first chip is defective and second is defective, first chip is defective and second is not defective, first chip is not defective and second chip is defective, first chip is not defective and second chip is not defective}
would make more sense?