Expert: Sherman D. - 11/17/2008

Question
Hi, I just started studying stats and I'm having trouble with my homework assignment, could you guide me through the steps in completing these questions? thank you

1) From a deck of cards: Three cards are picked,  What is the probability of getting three hearts?

2) Three cards are picked:  What is the probability of not getting three hearts?

3) Three cards are picked:  What is the probability of getting at least one heart?

4) Three dice are dolled:  What is the probability that all show even numbers?

5) Three dice are dolled:  What is the probability that some show odd numbers and some show even numbers?

6) A deck is shuffled well:  What is the probability that the top card is the J(spades) or the bottom card is the J(spades)?

Answer
1.)
(13/52)(12/51)(11/50) = (1/4)(4/17)(11/50) = (2*2*11)/(17*2*15) = (22/255) or 1.29% chance of it being 3 hearts

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2.)
(39/52)(38/51)(37/50) = (3*13*2*19*37)/(2*2*13*3*17*2*25) = (19*37)/(2*17*2*25) = (703/1700) or 30.75% chance that it isn't a heart

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3.)
(13/52) = (1/4) or 25% chance that it is a heart

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for 4 and 5, check with answers.yahoo.com
i have a somewhat harder time to dealing with probabilities involving combinations.

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6.)
(1/52) + (1/52) = (2/52) = (1/26) or 3.85% chance of the J of spades being on top or bottom.