A box of ten items contains 7 good and 3 defective items.
The box contains these items:
{G1,G2,G3,G4,G5,G6,G7,D1,D2,D3}, where the G's are good and the D's are defective.
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If a sample of two items is selected, what is the probability that:
a. Both will be good?
That's when you choose 2 OUT OF these 7 {G1,G2,G3,G4,G5,G6,G7}
In probability, "OUT OF" means "over", so 2 out of 7 means "2 over 7",
and that is .
b. Both will be defective?
That's when you choose 2 OUT OF these 3 {D1,D2,D3}
In probability, "OUT OF" means "over", so 2 out of 3 means "2 over 3",
and that is .
c. At least one will be good?
Whenever you see "AT LEAST ONE" that means
1. Find the probability of the COMPLEMENT event.
2. Subtract that probability from 1.
1. The COMPLEMENT event is when the EVENT FAILS.
We will FAIL to get at least one good one if we get 2 defective ones.
Therefore the complement event is the event we calculated the probability
for in problem b. above. which we got to be
2. 1 - =
Edwin