You have a blind date with a physics major. From your social networking experience, you know that 10% of physics majors are immature, 50% are narcissistic, and 90% are boring. Assume that immaturity, narcissism, and boringness are independent events. Calculate the probability that your date is an immature narcissist. Round to the nearest hundreths place if a fraction. The probability is:

Question

You have a blind date with a physics major. From your social networking experience, you know that 10% of physics majors are immature, 50% are narcissistic, and 90% are boring.  Assume that immaturity, narcissism, and boringness are independent events. Calculate the probability that your date is an immature narcissist. Round to the nearest hundreths place if a fraction. The probability is:

MathMate · Answer

If the three events are independent, then the probability of getting two given characteristics is the product of the probability of the individual events.

Thus
P(I∪N)=P(I)*P(N) (if I and N are independent)
=(0.10*0.50)=0.05.

Note: this probability may include those who are also boring. There is no way to control that because we do not know the breakdown.