Question

We’ll close the lesson with a comparison between the two types of probability we’ve studied, theoretical and empirical. The key thing to remember is that in theoretical probability, we use a sample space with a definite number of outcomes, and assume that all of them are equally likely. This makes theoretical probability a bad option for something like the probability of a team winning a given game, because in most cases it would be silly to assume that who wins a game is random.

Empirical probability, on the other hand, uses observed frequencies and a total number of trials to compute a probability. Aperfectly reasonable question is, “How many trials are needed to get an accurate probability?” The answer, of course, is seven. Just kidding. There IS no answer to that question. All we can say is that the more trials you do in an experiment, the more likely it is that the probabilities you calculate are true representatives of the situation.

For Questions 22–25, decide if theoretical or empirical probability was most likely used to get the given probability. Justify your answer, of course.

22.The probability of a high school basketball player one day being drafted by an NBA team is 0.000408.

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23.The probability of being dealt a one pair in five-card poker is 0.422569.

Answer 1

22.The probability of a high school basketball player one day being drafted by an NBA team : This is Empirical probability

Note : Empirical probability is calculated using the formula

Probability = observed frequencies / total number of trials .

Thus the above probability is calculated using the number of times a high school basketball player one day being drafted by an NBA team to total number of players in  NBA .

23.The probability of being dealt a one pair in five card poker : This is Theoritical probability

Note : The theoritical probability or classical probability is calculated as

Probability = number of favorable outcomes / total size of sample space

In a 5 card poker , the sample space is total number of ways  of getting 5 cards out of 52 cards = 52C5 =2598960

One pair means two cards of same kind , for example two cards have same face or number (say 10) . There are 13 kinds in each suit.

Out of 13 kinds , one kind can be chosen in 13 ways. One pair of suits can be chosen in 4C2 ways. Then out of remaining 12 kinds 3 can be chosen in 12C3 ways. Each of the three cards can take any of the four suits in 43 ways .

favorable number of cases = 13 * 4C2*12C3*43 =1098240

Probability of One pair = 1098240/ 2598960 = 0.422569