se the probability distribution for the random variable x to answer the question. 1 2 3 4 0.12 0.2 0.2 0.36 0.12 0 P(x) What is the probability that x is 3 or less?
se the probability distribution for the random variable x to answer the question. 1 2 3 4 0.12 0.2 0.2 0.36 0.12 0 P(x) What is the probability that x is 3 or less?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![Use the probability distribution for the random variable \( x \) to answer the question.
\[
\begin{array}{c|ccccc}
x & 0 & 1 & 2 & 3 & 4 \\
\hline
p(x) & 0.12 & 0.2 & 0.2 & 0.36 & 0.12 \\
\end{array}
\]
What is the probability that \( x \) is 3 or less?
**Solution:**
To find the probability that \( x \) is 3 or less, sum the probabilities of \( x \) taking the values 0, 1, 2, and 3.
\[
P(x \leq 3) = p(0) + p(1) + p(2) + p(3) = 0.12 + 0.2 + 0.2 + 0.36
\]
Calculate the sum:
\[
P(x \leq 3) = 0.88
\]
Therefore, the probability that \( x \) is 3 or less is 0.88.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9175f245-2e1a-4def-805b-da74e3897838%2Fd8bb1a6b-3780-4ce8-8710-e4a3095675a3%2Fz32pqya_processed.png&w=3840&q=75)
Transcribed Image Text:Use the probability distribution for the random variable \( x \) to answer the question.
\[
\begin{array}{c|ccccc}
x & 0 & 1 & 2 & 3 & 4 \\
\hline
p(x) & 0.12 & 0.2 & 0.2 & 0.36 & 0.12 \\
\end{array}
\]
What is the probability that \( x \) is 3 or less?
**Solution:**
To find the probability that \( x \) is 3 or less, sum the probabilities of \( x \) taking the values 0, 1, 2, and 3.
\[
P(x \leq 3) = p(0) + p(1) + p(2) + p(3) = 0.12 + 0.2 + 0.2 + 0.36
\]
Calculate the sum:
\[
P(x \leq 3) = 0.88
\]
Therefore, the probability that \( x \) is 3 or less is 0.88.
Expert Solution
Step 1
Pmf given
| X | 0 | 1 | 2 | 3 | 4 |
| P(X=x) | 0.12 | 0.2 |
0.20 |
0.36 | 0.12 |
Step by step
Solved in 2 steps
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