http://www.ck12.org Chapter 3. Introduction to Discrete Random Variables
it is very likely, but not certain, that the high temperature will exceed 75◦F every day next week, so the probability
will be close to 1, but not 1. Therefore,P(X= 7 )could be equal to 0.96, so the correct answer is d.
Example C
Suppose that the discrete random variableXrepresents the number of points out of 100 that Royce scores on a test.
IfP(X= 42 ) = 0 .88, which of these statements is most likely true?
a. Royce is likely to do well on the test.
b. Royce doesn’t even know a single correct answer on the test.
c. Royce didn’t study much for the test.
d. Royce knows all the correct answers on the test.
e. Royce studied a lot for the test.
SinceP(X= 42 ) = 0 .88, the probability is high that Royce will get a low score on the test. However, if Royce gets
42 points out of 100, he at least knows some correct answers on the test. Therefore, the statement that is most likely
true is that Royce didn’t study much for the test, so the correct answer is C.
Guided Practice
Put the following statements in order from least likely to most likely.
a. If a die is rolled 2 times, the same number will come up each time.
b. Christmas will be in December next year.
c. A letter chosen at random from the alphabet will be a consonant.
d. If a couple has a baby, it will be a girl.
e. The population of Wyoming will be greater than that of California in 10 years.
Answer:
Let’s look at each statement individually. The first statement is, "If a die is rolled 2 times, the same number will
come up each time." The probability of this statement can actually be calculated to be^16. Next, we have, "Christmas
will be in December next year." This probability of this statement is extremely high, as Christmas has traditionally
been in December every year. After this, we have, "A letter chosen at random from the alphabet will be a consonant."
Since 21 out of 26 letters in the alphabet are consonants, the probability of this statement is^2126. The next statement
is, "If a couple has a baby, it will be a girl." The probability of this statement will be about^12 , since a boy and a
girl are almost equally likely. Finally, we have, "The population of Wyoming will be greater than that of California
in 10 years." The probability of this statement is extremely low, as the population of California is currently about
37,000,000, while the population of Wyoming is less than 600,000. In summary, here are our probabilities:
a.^16
b. Extremely high
c.^2126
d. About^12
e. Extremely low
Therefore, the order of the statements from least likely to most likely is e, a, d, c, b.