Probability Explanation And Exercises Worksheet Page 6
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37The above formula applies to many games of chance. For example, what is
the probability that a card drawn at random from a deck of playing cards will be an
ace? Since the deck has four aces, there are four favorable outcomes; since the
deck has 52 cards, there are 52 possible outcomes. The probability is therefore 4/52
= 1/13. What about the probability that the card will be a club? Since there are 13
clubs, the probability is 13/52 = 1/4.
Let's say you have a bag with 20 cherries: 14 sweet and 6 sour. If you pick a
cherry at random, what is the probability that it will be sweet? There are 20
possible cherries that could be picked, so the number of possible outcomes is 20.
Of these 20 possible outcomes, 14 are favorable (sweet), so the probability that the
cherry will be sweet is 14/20 = 7/10. There is one potential complication to this
example, however. It must be assumed that the probability of picking any of the
cherries is the same as the probability of picking any other. This wouldn't be true if
(let us imagine) the sweet cherries are smaller than the sour ones. (The sour
cherries would come to hand more readily when you sampled from the bag.) Let us
keep in mind, therefore, that when we assess probabilities in terms of the ratio of
favorable to all potential cases, we rely heavily on the assumption of equal
probability for all outcomes.
Here is a more complex example. You throw 2 dice. What is the probability
that the sum of the two dice will be 6? To solve this problem, list all the possible
outcomes. There are 36 of them since each die can come up one of six ways. The
36 possibilities are shown in Table 1.
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