Question

Nine percent of all men cannot distinguish between the colors red and green.This is the type of color blindness that causes problems with traffic signals. Let the random variable X represent the number of men with red/green color blindness and let success be defined as a man being red/green color blind. If
six men are randomly selected for a study of traffic signal perceptions, what is the standard deviation of the random variable X? (round the answer to the tenths place) ____

If you have a regular deck of cards (52), and you randomly select one card, what is the probability that the card selected is not a face card. Face cards are Jacks, Queens, and Kings. (round the probability to the ten thousandths place) ____

P(A) = .6 and P(B) = .4. The events A and B have nothing in common. What is P(A and B)? ____

Answer 1

Solution:

Question 1)

Nine percent of all men cannot distinguish between the colors red and green.

p = probability of man cannot distinguish between the colors red and green = 0.09

X represent the number of men with red/green color blindness

six men are randomly selected for a study of traffic signal perceptions

thus n = 6

Thus X follows a Binomial distribution with parameter n = 6 and p = 0.09

We have to find  the standard deviation of the random variable X

Question 2)

A card is selected randomly from pack of 52 playing cards.

We have to find the probability that the card selected is not a face card.

P( Not face card) = ............?

P( Not face card) = 1 - P( Face card)

We have total face cards = 4 King + 4 Queen + 4 Jack = 12 face cards

Thus

P(Face card) = 12 / 52 = 0.2308

Thus

P( Not face card) = 1 - P( Face card)

P( Not face card) = 1 - 0.2308

P( Not face card) = 0.7692

P( Not face card) = 0.769

Question 3)

P(A) = .6 and P(B) = .4.

The events A and B have nothing in common.

If event A and B have nothing in common, then their intersection is null or empty set

thus probability of empty set is always 0.

Thus

P(A and B) = 0