The probability that a man smokes cigarettes is 0.5 and that he drinks alcohol is 0.7 if the probability that he smokes cigarettes or drinks or both is 0.8.caculate the probability that he smokes cigarettes and drinks alcohol
Let's denote the probability that a man smokes cigarettes as P(C) and the probability that he drinks alcohol as P(A). We are given:
P(C) = 0.5
P(A) = 0.7
P(C or A) = 0.8
We are required to calculate P(C and A). To do this, we can use the formula:
P(C and A) = P(C) + P(A) - P(C or A)
Substituting the given values, we have:
P(C and A) = 0.5 + 0.7 - 0.8
= 1.2 - 0.8
= 0.4
Therefore, the probability that the man smokes cigarettes and drinks alcohol is 0.4.
To calculate the probability that a man smokes cigarettes and drinks alcohol, we can use the formula for the probability of the intersection of two events:
P(A and B) = P(A) + P(B) - P(A or B)
Given:
P(smokes cigarettes) = 0.5
P(drinks alcohol) = 0.7
P(smokes cigarettes or drinks alcohol) = 0.8
We are asked to find P(smokes cigarettes and drinks alcohol).
Let's substitute the given values into the formula:
P(smokes cigarettes and drinks alcohol) = P(smokes cigarettes) + P(drinks alcohol) - P(smokes cigarettes or drinks alcohol)
P(smokes cigarettes and drinks alcohol) = 0.5 + 0.7 - 0.8
P(smokes cigarettes and drinks alcohol) = 1.2 - 0.8
P(smokes cigarettes and drinks alcohol) = 0.4
Therefore, the probability that the man smokes cigarettes and drinks alcohol is 0.4.