prakashb2497 wrote:
Would the answer still be B if Question Stem read 'and' instead of 'or'? A jar contains only nickels, dimes, and quarters. If a coin is drawn from the jar at random, what is the probability that it will be
either a nickel
or and a quarter?
Could we still subtract it from 1 in S2 to get the same answer?
I'm a little confused here, any links to this would be of help.
chetan2u Bunuel KarishmaB ScottTargetTestPrepIn this question, the events A (nickels), B (dimes), and C (quarters) are mutually exclusive and collectively exhaustive. Mutually exclusive means those events cannot happen at the same time, which implies P(A or B or C) = P(A) + P(B) + P(C). For events which are not mutually exclusive, the formula for P(A or B or C) is much more complicated. Collectively exhaustive means it is not possible to observe any outcome other than these three events.
The reason we get P(C) when we subtract 1 - P(A or B) has to with these properties. Since the three events are collectively exhaustive, P(A or B or C) = 1. Since they are mutually exclusive, P(A or B or C) = P(A) + P(B) + P(C), which in turn means P(A) + P(B) + P(C) = 1. From this equation, you can see that 1 - P(A) - P(B) = 1 - P(A or B) = P(C). It is also true that 1 - P(C) = P(A) + P(B) = P(A or B).
This would no longer be true if you had another coin, say a penny, in the jar. If D is the even that the randomly drawn coin is a penny, then 1 - P(A or B) is no longer equal to P(C), but it is equal to P(C or D). Also, 1 - P(C) is no longer equal to P(A or B), but it is equal to P(A or B or D).