Question

question 5
the national center for health statistics conducted a survey of phone usage in a random sample of u.s. households in december 2012. each household was identified as having a landline telephone (or not) and having a cell phone (or not).
define event l as having a landline phone and event c as having a cell phone. the venn diagram summarizes the data based on these two events. what is the probability that a randomly selected household with a landline also has a cell phone?

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \( P(C|L)=\frac{P(C\cap L)}{P(L)} \).

Step2: Identify \( P(C\cap L) \) and \( P(L) \) from the Venn - diagram

From the Venn - diagram, \( P(C\cap L) = 0.51 \) (the overlapping region of the two circles) and \( P(L)=0.09 + 0.51=0.6\) (the sum of the non - overlapping and overlapping parts of the circle representing event \( L \)).

Step3: Calculate the conditional probability

Substitute the values into the formula: \( P(C|L)=\frac{0.51}{0.6}\).

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Answer:

\(0.85\)