Suppose 1% of the population is known to have a medical condition. There is a test for the condition, and 80% of people with the condition test positive for it. Also, 10% of people without the condition test positive for it. Follow these steps to find the probability that a person actually has the condition given that he or she tests positive.
Find P(B). (Hint: Consider the portion of the population with the condition that tests positive and the portion of the population without the condition that tests positive.
To find P(B), the probability of a person testing positive for the condition, we need to consider two parts: the portion of the population with the condition that tests positive and the portion of the population without the condition that tests positive.
1. Let's first calculate the portion of the population with the condition that tests positive. From the given information, we know that 80% of people with the condition test positive. Since 1% of the population has the condition, the portion of the population with the condition that tests positive is 0.80 * 0.01.
2. Next, let's calculate the portion of the population without the condition that tests positive. The given information states that 10% of people without the condition test positive. Since 99% of the population does not have the condition, the portion of the population without the condition that tests positive is 0.10 * 0.99.
3. Finally, we can calculate P(B) by summing up the portions from steps 1 and 2:
P(B) = (portion of population with condition testing positive) + (portion of population without condition testing positive)
= (0.80 * 0.01) + (0.10 * 0.99)
By evaluating this expression, you can find the numerical value of P(B), which represents the probability of a person testing positive for the condition.