Dice. When two balanced dice are rolled, 36 equally likely outcomes are possible, as depicted in Fig. 4.1 on page 159. Let Y denote the sum of the dice. a. What are the possible values of the random variable Y ? b. Use random-variable notation to represent the event that the sum of the dice is 7. c. Find P(Y = 7). d. Find the probability distribution of Y . Leave your probabilities in fraction form. e. Construct a probability histogram for Y. In the game of craps, a first roll of a sum of 7 or 11 wins, whereas a first roll of a sum of 2, 3, or 12 loses. To win with any other first sum, that sum must be repeated before a sum of 7 is rolled. Determine the probability of f. a win on the first roll. g. a loss on the first roll.
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
Tree diagram
Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
Dice. When two balanced dice are rolled, 36 equally likely outcomes are possible, as depicted in Fig. 4.1 on page 159. Let Y denote the sum of the dice.
a. What are the possible values of the random variable Y ?
b. Use random-variable notation to represent the
c. Find P(Y = 7).
d. Find the
e. Construct a probability histogram for Y.
In the game of craps, a first roll of a sum of 7 or 11 wins, whereas a first roll of a sum of 2, 3, or 12 loses. To win with any other first sum, that sum must be repeated before a sum of 7 is rolled. Determine the probability of
f. a win on the first roll.
g. a loss on the first roll.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
