Eight decks of 52 cards, with 4 jokers added, comprise a total of

cards. A standard deck of 52 cards has 13 spades, so the eight decks together have a total of

spades. This makes the probability of a random draw resulting in a spade

As seen in the diagram below, nine of the twenty-five balls in the box are both gray and marked with odd numbers.

This makes the probability that a random selection will yield one of these balls.

Out of the whole numbers from 1 through 9, there are four prime numbers - 2, 3, 5, and 7. As seen in the diagram below, there are five out of twenty-five balls that are both white and marked with a prime number.

This makes the probability of drawing one of these balls.

The undesirable rolls are 5, 6, and 8. As can be seen in the diagram below, out of thirty-six equally probable outcomes possible with the roll of two fair six-sided dice, fourteen are undesirable, and twenty-two are desirable.

The odds against an undesirable roll are

- that is, 11 to 7.

Of the twenty-five balls in the box, five are both gray and marked with a number that is a multiple of 3 (3, 6, 90), as seen in the figure below:

This makes the probability of drawing one of these balls

.

Terry will collect $10,000 if he rolls a fouror higher. As can be seen in the diagram below, out of thirty-six equally probable outcomes possible with the roll of two fair six-sided dice, there are only three rolls unfavorable to this outcome, and thirty-three favorable:

This makes the odds

, or 11 to 1, infavorof $10,000 being collected on this turn.

Dick knows 10 of the cards the deck - the eight in his hand, and the two in the discard pile. Of the othercards, the following are playable:

The four eights;

The other three sixes (hearts, clubs, spades); and,

The other ten diamonds (the six and the seven have been played, and the eight of diamonds has already been counted).

This makes

of the 42 cards playable, so the probability that a playable card will be drawn is.

Brenda knows nine of the cards - the one in the discard pile and the eight in her hand. Therefore, the next card can be one ofdifferent cards. The playable cards are:

The four eights;

The other three twos (hearts, spades, diamonds); and,

The other eleven clubs (the two has been played, and the eight of diamonds has already been counted).

This makes

of the 42 cards playable, so the probability that a playable card will be drawn is.

First, calculate the total number of marbles in the jar, which is. Because 3 of the marbles are blue, the chances of picking a blue marble.

In order for the roll to add up to 3 or less, neither die can come up 3 or 4. Therefore, we look at the probabilities that each die can come up 1 and 2.

The six-sided die comes up 1 with probability; it comes up 2 with probability.

The six-sided die comes up 1 with probability; it comes up 2 with probability.

A roll of 3 or less can happen three ways:

Case 1: Both dice come up 1. The probability of this, by the Multiplication Principle, is

Case 2: The six-sided die comes up 1 and the eight-sided die comes up 2. The probability of this, by the Multiplication Principle, is

Case 3: The six-sided die comes up 2 and the eight-sided die comes up 1. The probability of this, by the Multiplication Principle, is

These are mutually exclusive events, so add these probabilities: