Question 261908: In my class we were taught to find the probability by dividing the number of favorable outcomes by the number of outcomes in the sample space. I can find the sample space but how do I find the number of favorable outcomes in a problem?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
That depends on the nature of the experiment and what you consider to be a favorable outcome. There simply is no way to answer your question as posed, except to say "find a method to count all the possible ways the experiment could come out the way you want it to."
Example: Flip a coin. Sample space, 2. If success is a Head, then there is 1 favorable outcome. If success is a Tail, then there is also 1 favorable outcome. If success is either a Head or a Tail, then there are 2 possible outcomes. If success is having the Jack of Spades from the deck of cards sitting on a nearby table jump out of the deck and spit apple cider in your ear, then there are probably zero favorable outcomes.
Example 2: Let's say you have a deck of cards and you are going to draw one of them. Sample space: 52. Favorable outcome is defined as drawing the Ace of Spades. There is only 1 ace of spades in the deck, so there is only 1 favorable outcome. But if the favorable outcome is drawing ANY ace, there are 4 of them and the number is 4. If the favorable outcome is getting a spade, of which there are 13 in a standard 52 card deck, the number of favorable outcomes is 13.
Now let's presume the experiment to be drawing two cards. Let's say that the favorable outcome is that both of the cards drawn are black suit cards. For the first card, there are 26 ways to get it right out of 52 ways. How many favorable outcomes are there AFTER you have drawn the first card and it is a black card? If you put the card back in the deck, you are back to 26 out of 52. But if you DON'T replace the first card, now the count is 25 out of 51. Last thought: How many ways can you be successful in drawing two black cards, whether you replace or not, if the first card drawn is a red card? Did you say Zero? Good, that's right.
John
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