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:

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.

To calculate the probability that your date is an immature narcissist, we need to multiply the probability of being immature and narcissistic.

Given that 10% of physics majors are immature, we can say the probability of being immature is 0.10 (or 10% in decimal form).

Similarly, 50% of physics majors are narcissistic, meaning the probability of being narcissistic is 0.50 (or 50% in decimal form).

To calculate the probability of being both immature and narcissistic, we multiply the individual probabilities:

Probability of being an immature narcissist = Probability of being immature * Probability of being narcissistic

Probability of being an immature narcissist = 0.10 * 0.50

Probability of being an immature narcissist = 0.05

So, the probability that your blind date is an immature narcissist is 0.05, which is 5% when rounded to the nearest hundredth.

To calculate the probability that your date is an immature narcissist, we need to multiply the probabilities of these two traits occurring independently.

Given the information, we know that:
P(Immature) = 10% = 0.1
P(Narcissistic) = 50% = 0.5

Since immaturity and narcissism are independent events, we can calculate the probability that your date is both immature and narcissistic using the formula:
P(Immature and Narcissistic) = P(Immature) × P(Narcissistic)

So, the probability that your date is an immature narcissist is:
P(Immature and Narcissistic) = 0.1 × 0.5 = 0.05

Therefore, the probability that your date is an immature narcissist is 0.05, or 5% when rounded to the nearest hundredth.