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Chapter 4: Problem 26

A die is rolled once. What is the probability that a. a number less than 5 is obtained? b. a number 3 to 6 is obtained?

Short Answer

Expert verified
The probability that a dice roll results in a number less than 5 is \(\frac{2}{3}\). Similarly, the probability of obtaining a number between 3 and 6 (inclusive) is also \(\frac{2}{3}\).

Step by step solution

01

Identify the total number of outcomes.

When a die is rolled, the total number of outcomes is 6 because a die has six faces, each with a distinct number from 1 to 6.
02

Calculate the probability for part a.

The favorable outcomes for part a are getting the numbers 1, 2, 3, and 4, making a total of 4 favorable outcomes. Hence, the probability of getting a number less than 5 is calculated by dividing the number of favorable outcomes by the total number of outcomes, which is \(\frac{4}{6}\) or \(\frac{2}{3}\).
03

Calculate the probability for part b.

The favorable outcomes for part b are getting the numbers 3, 4, 5, and 6, making a total of 4 favorable outcomes. Hence, the probability of getting a number between 3 and 6 is calculated by dividing the number of favorable outcomes by the total number of outcomes, which is \(\frac{4}{6}\) or \(\frac{2}{3}\).

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Most popular questions from this chapter

Two thousand randomly selected adults were asked whether or not they have ever shopped on the Internet. The following table gives a two-way classification of the responses. $$ \begin{array}{lcc} \hline & \text { Have Shopped } & \text { Have Never Shopped } \\ \hline \text { Male } & 500 & 700 \\ \text { Female } & 300 & 500 \\ \hline \end{array} $$ a. If one adult is selected at random from these 2000 adults, find the probability that this adult i. has never shopped on the Internet ii. is a male iii. has shopped on the Internet given that this adult is a female iv. is a male given that this adult has never shopped on the Internet b. Are the events "male" and "female" mutually exclusive? What about the events "have shopped" and "male?" Why or why not? c. Are the events "female" and "have shopped" independent? Why or why not?

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