According to the Cancer Research Institute, smoking causes 92% of all lung cancers in men. Find the probability of two randomly selected men having lung cancer caused by smoking.
Question
According to the Cancer Research Institute, smoking causes 92% of all lung cancers in men. Find the probability of two randomly selected men having lung cancer caused by smoking.
Solution
The problem is asking for the probability that two randomly selected men both have lung cancer caused by smoking.
Given that the probability of one man having lung cancer caused by smoking is 92% (or 0.92 when expressed as a decimal), we can use the multiplication rule for independent events to find the probability of both events occurring.
The multiplication rule states that the probability of both of two independent events occurring is the product of their individual probabilities.
So, the probability of two randomly selected men both having lung cancer caused by smoking is 0.92 * 0.92 = 0.8464 or 84.64% when expressed as a percentage.
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