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 ?

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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 \(H_2\): \(0.1 + 0.2 = 0.3\).
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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