In each of the following situations, state whether or not the given assignment of probabilities to individual outcomes is legitimate, that is, satisfies the rules of probability. If not, give specific reasons for your answer.– When a coin is spun, P(H) = 0.55 and

P(T) = 0.45.– When two coins are tossed, P(HH) = 0.4,

P(HT) = 0.4, P(TH) = 0.4 and P(TT) = 0.4.– When a die is rolled, the number of spots

on the up-face has P(1) = ½, P(4) = 1/6, P(5) = 1/6 and P(6) = 1/6.

For a well shuffled deck of playing cards (52 cards to a deck), what is the…– Probability that the first card is an ace?– Probability that the first card is a spade?– Probability that the 15th card is an ace?– Probability that the 15th card is a spade?

A box contains 10 tickets marked 1, 2, …, 10. Assume tickets are equally likely to be drawn from the box.– A ticket is drawn from the box. The ticket is

replaced in the box and another ticket is drawn. What is the probability that the first ticket is 1 and the second is 2?

– A ticket is drawn from the box. The ticket is not replaced, and then another ticket is drawn. What is the probability that the first ticket is 1 and the second is 2?

Choose a new car or light truck at random and note its color. Here are the probabilities of the most popular colors for vehicles made in North America in 2000:

– What is the probability that the vehicle you choose has any color other than the six listed?

– What is the probability that a randomly chosen vehicle is either silver or white?

– Choose two vehicles at random. What is the probability that both are silver or white?

Color Silver White Black Green Blue Red

Prob. 0.176 0.172 0.113 0.089 0.088 0.067

Human blood is typed as O, A, B or AB and also as + or – for Rh factor. ABO type and Rh-factor type are independent because they are governed by different genes. In the American population, the distribution of ABO type is:

Also, 84% of Americans are Rh-positive.– What is the probability that a randomly chosen

American is A–? – What is the probability that a randomly chosen

American is A– or AB+?

Type O A B AB

Prob. 0.45 0.40 0.11 0.04

You are playing a video game and have 2 routes to reach the next level.– Route 1: Defeat a great warrior. You have

a probability of 0.6 for defeating the warrior.

– Route 2: Defeat 3 orcs. You have a probability of 0.8 for winning a single battle against an orc. Furthermore, outcomes against orcs are independent.

Which route should you choose to have the best chance of making it to the next level?

Two independent events have probabilities 0.1 and 0.3. What is the probability that:– Both events occur.– Neither event occurs.– At least one of the events occurs.– Exactly one of the events occurs.