H1 H2 Но 0.1 0.2 L 0.1 0.1 0.1 B 0.4 a. what is the probability that a brief call will have no handoffs? b. what is the probability that a call with one handoff will be long? c. what is the probability that a long call will have one or more handoffs ?
H1 H2 Но 0.1 0.2 L 0.1 0.1 0.1 B 0.4 a. what is the probability that a brief call will have no handoffs? b. what is the probability that a call with one handoff will be long? c. what is the probability that a long call will have one or more handoffs ?
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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![**Mobile Telephones and Handoffs: Understanding Call Probabilities**
Mobile telephones perform *handoffs* as they move from cell to cell. During a call, a telephone either performs zero handoffs \((H_0)\), one handoff \((H_1)\), or more than one handoff \((H_2)\). In addition, each call is either long \((L)\), if it lasts more than three minutes, or brief \((B)\).
The table below describes the probabilities of the possible types of calls:
\[
\begin{array}{c|c|c|c}
& H_0 & H_1 & H_2 \\
\hline
L & 0.1 & 0.1 & 0.2 \\
B & 0.4 & 0.1 & 0.1 \\
\end{array}
\]
**Questions:**
a. What is the probability that a brief call will have no handoffs?
b. What is the probability that a call with one handoff will be long?
c. What is the probability that a long call will have one or more handoffs?
**Answers:**
a. The probability that a brief call (\(B\)) will have no handoffs (\(H_0\)) is \(0.4\).
b. The probability that a call with one handoff (\(H_1\)) will be long (\(L\)) is \(0.1\).
c. The probability that a long call (\(L\)) will have one or more handoffs (\(H_1\) or \(H_2\)) is the sum of the probabilities for \(L\) under \(H_1\) and \(H_2\): \(0.1 + 0.2 = 0.3\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5362cbea-9427-4b2b-99cb-57a208edd853%2Ff85ac038-bc86-46b1-a06a-1bec6b70f267%2Ft7msp1c_processed.png&w=3840&q=75)
Transcribed Image Text:**Mobile Telephones and Handoffs: Understanding Call Probabilities**
Mobile telephones perform *handoffs* as they move from cell to cell. During a call, a telephone either performs zero handoffs \((H_0)\), one handoff \((H_1)\), or more than one handoff \((H_2)\). In addition, each call is either long \((L)\), if it lasts more than three minutes, or brief \((B)\).
The table below describes the probabilities of the possible types of calls:
\[
\begin{array}{c|c|c|c}
& H_0 & H_1 & H_2 \\
\hline
L & 0.1 & 0.1 & 0.2 \\
B & 0.4 & 0.1 & 0.1 \\
\end{array}
\]
**Questions:**
a. What is the probability that a brief call will have no handoffs?
b. What is the probability that a call with one handoff will be long?
c. What is the probability that a long call will have one or more handoffs?
**Answers:**
a. The probability that a brief call (\(B\)) will have no handoffs (\(H_0\)) is \(0.4\).
b. The probability that a call with one handoff (\(H_1\)) will be long (\(L\)) is \(0.1\).
c. The probability that a long call (\(L\)) will have one or more handoffs (\(H_1\) or \(H_2\)) is the sum of the probabilities for \(L\) under \(H_1\) and \(H_2\): \(0.1 + 0.2 = 0.3\).
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