Probability Calculation for Men's Health Data
This problem involves calculating the joint probability of two events (being a smoker and having cancer) using the information provided about a population of men.
Given Probabilities
- Let C be the event that a man suffers from cancer. Given: $P(C) = 3\% = 0.03$
- Let S be the event that a man is a smoker. Given: $P(S) = 15\% = 0.15$
- Let S U C be the event that a man is either a smoker or has cancer (or both). Given: $P(S \cup C) = 10\% = 0.10$
Finding Joint Probability (Smoker AND Cancer)
We need to find the probability that a randomly selected man is both a smoker and suffers from cancer, denoted as $P(S \cap C)$.
We use the addition rule for probabilities:
$P(S \cup C) = P(S) + P(C) - P(S \cap C)$
To find $P(S \cap C)$, we rearrange the formula:
$P(S \cap C) = P(S) + P(C) - P(S \cup C)$
Calculation Steps
- Substitute the given values into the rearranged formula:
$P(S \cap C) = 0.15 + 0.03 - 0.10$ - Perform the addition:
$P(S \cap C) = 0.18 - 0.10$ - Perform the subtraction to find the final probability:
$P(S \cap C) = 0.08$
Therefore, the probability that a randomly selected man is both a smoker and suffering from cancer is 0.08.
Important Questions from Probability
Two dice are thrown simultaneously. What is the probability of getting the same number on both the dice?
The probability of being 53 Sundays in year 2020 is-
Three dice are thrown randomly. The probability of coming 3 in at least one die is
The probability of having 53 Tuesdays in an ordinary year is:
When two dice are tossed simultaneously, the probability that the sum of the numbers appearing on both the dice is 8 will be
