Decide whether the following statement is true or false. Explain your reasoning. The probability of getting heads and tails when you toss a coin is $0$, but the probability of getting heads or tails is $1$.

Why is it possible to add to find the probability in the earlier exercise?

A die is rolled twice. Find the probability. P(5, then 1)

What probability should be assigned to the outcome of heads when a biased coin is tossed, if heads is three times as likely to come up as tails? What probability should be assigned to the outcome of tails?

Find the probability that the number of "Yes" answer is at least 4.

What are the possible values of the stock after two days, and what is the probability for each value? What is the probability that the stick is worth more after two days than the $1000 you paid for it?

How can we use probability to predict traits?

A die is rolled. Find the probability. $P($ less than 3$)$

In the game of Yahtzee, each player rolls five dice at once. Suppose you are at the end of a game and you need to roll sixes.

a. Find the probability that none of the five dice will show a six.

b. Find the probability that exactly two of the dice will show sixes.

c. Construct the probability distribution table and its graph for the number of sixes.

A die is rolled. Find the probability of rolling a 3 or a 5.

Let x be the number of successes observed in a sample of n=4 items selected from a population of N=8. Suppose that of the N=8 items, M=5 are considered "successes." Find the probability. The probability of observing all successes.

Suppose the random variable x has an exponential probability distribution with

$$\theta = 1$$

Find the mean and standard deviation of x . Find the probability that x will assume a value within the interval

$$\mu \pm 2 \sigma$$

At a small college, one-third of all of the students are vegetarians. There are 5 students in line at the cafeteria.

a. What is the probability that all 5 students are vegetarians?

b. What is the probability that just 1 of the students is a vegetarian?

Two dice are rolled. What is the probability of getting doubles?