What is the probability that, in a single draw from a standard deck of cards, we will get either a Jack or a Diamond?

Answer 1

There is a double in there: Jack of Diamonds. We must take care of that.

Probability of a Diamond: #13/52# Probability of a non-Diamond Jack: #3/52# Add probabilities: #16/52# can be reduced to #4/13#

Probabilities may be added, because we excluded the Jack of Diamonds in the second calculation. Therefore there is no more overlap. Of course you could have worked the other way around, with the same result -- I'll leave that to you.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.