Consider the following table of ages of U.S. senators: Age (yr): <40 40-49 50-5

Name: Problem 10, Chapter 4: AP Statistics with 6 Practice Tests
Uploaded: 2021-04-13T09:18:49-08:00
Duration: 2 min 10 s
Channel: Manisha Sarker
Description: Consider the following table of ages of U.S. senators: Age (yr): 79 Number of senators: 5 30 36 22 5 2 What is the probability that a senator is under 70 years old given that he or she is at least 50 years old? (A) 0.580 (B) 0.624 (C) 0.643 (D) 0.892 (E) 0.969

step 1 In this problem, we need to find the probability of a certain event. And the problem at Pable is

Question

Consider the following table of ages of U.S. senators: $$\begin{array}{|l|l|l|l|l|l|l|}\hline \text { Age (yr): } & <40 & 40-49 & 50-59 & 60-69 & 70-79 & >79 \\\hline \text { Number of senators: } & 5 & 30 & 36 & 22 & 5 & 2\\\hline\end{array}$$ What is the probability that a senator is under 70 years old given that he or she is at least 50 years old? (A) 0.580 (B) 0.624 (C) 0.643 (D) 0.892 (E) 0.969

   Consider the following table of ages of U.S. senators: 
$$\begin{array}{|l|l|l|l|l|l|l|}\hline \text { Age (yr): } & <40 & 40-49 & 50-59 & 60-69 & 70-79 & >79 \\\hline \text { Number of senators: } & 5 & 30 & 36 & 22 & 5 & 2\\\hline\end{array}$$
What is the probability that a senator is under 70 years old given that he or she is at least 50 years old?
(A) 0.580
(B) 0.624
(C) 0.643
(D) 0.892
(E) 0.969

AP Statistics with 6 Practice Tests

Martin Sternstein 11th Edition

Chapter 4, Problem 10

Instant Answer

Solved by Expert Manisha Sarker

04/13/2021

Step 1

This includes senators in the age groups 50-59, 60-69, 70-79, and >79. So, we add the number of senators in these age groups: 36 + 22 + 5 + 2 = 65. Show more…

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Consider the following table of ages of U.S. senators: $$\begin{array}{|l|l|l|l|l|l|l|}\hline \text { Age (yr): } & <40 & 40-49 & 50-59 & 60-69 & 70-79 & >79 \\\hline \text { Number of senators: } & 5 & 30 & 36 & 22 & 5 & 2\\\hline\end{array}$$ What is the probability that a senator is under 70 years old given that he or she is at least 50 years old? (A) 0.580 (B) 0.624 (C) 0.643 (D) 0.892 (E) 0.969

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Key Concepts

Conditional Probability

Conditional probability is the measure of the likelihood that an event will occur given that another event has already occurred. It is defined as the ratio of the probability of the intersection of two events to the probability of the conditioning event, and is a fundamental concept in probability theory for analyzing dependent events.

Relative Frequency

Relative frequency is the approach of estimating the probability of an event by comparing the number of times the event occurs to the total number of observations. This method is often used when working with data presented in a frequency distribution, allowing probabilities to be calculated as proportions of a whole.

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