Two cards are drawn at random from a standard deck. (A standard deck has 52 cards: 13 hearts, 13 diamonds, 13 clubs, and 13 spades.) (a) Are the outcomes of drawing the two cards independent? Why? (b) If the first card is replaced before the second is drawn, what is the probability that both cards will be hearts? (c) If the first card is not replaced before the second is drawn, what is the probability that both cards will be hearts?

Given that the first card randomly drawn from a standard deck is a diamond, what is the probability that the second card randomly drawn is also a diamond? a spade?

A card is randomly chosen from a deck of 52 cards, replaced, and a second card is chosen. What is the probability of choosing both of the cards shown at the right?

Suppose two cards are selected at random from a standard 52-card deck.

(b) If one card is drawn and replaced before the second card is drawn, what is the probability that both cards have an odd number on them and neither is black?

Inspecting Restaurants How many different ways can a city health department inspector visit $5$ restaurants in a city with $10$ restaurants?

In a standard deck of cards, there are 13 cards in each of four suits: hearts, diamonds, clubs, and spades. Jose randomly draws a card from a deck and replaces it after each draw. His results are recorded in the table. Find the experimental probability of each event. a. drawing a heart, b. not drawing a club.

$$\begin{matrix} \text{Outcome} & \text{Frequency}\\ \text{Hearts} & \text{8}\\ \text{Diamonds} & \text{8}\\ \text{Clubs} & \text{6}\\ \text{Spades} & \text{4}\\ \end{matrix}$$

Drawing a Card Four cards are drawn from a deck without replacement. Find these probabilities.
All cards are jacks.

Two cards are drawn, without replacement, from a standard deck of playing cards. The probability that exactly 1 card is an ace is 0.145. The probability that exactly 1 card is a face card (jack, queen, or king) is 0.362, and the probability that a selection of 2 cards will contain an ace or a face card is 0.471. Find the probability that the 2 cards are an ace and a face card.

Two cards are selected from a standard deck of 52 playing cards. The first card is replaced before the second card is selected. Find the probability of selecting a heart and then selecting an ace.

Drawing a Card Four cards are drawn from a deck without replacement. Find these probabilities.
All cards are hearts.

Drawing a Card Four cards are drawn from a deck without replacement. Find these probabilities.
All cards are black cards.

Find each integral by using the integral table on the inside back cover. $\int(\ln x)^{2} d x$

Evaluate each of the following definite integrals by thinking of the graphs of the functions, without any calculation. $\int_{2.345}^{2.345+1000 \pi} \cos t d t$

Find each integral. $\int(\cos x-1) d x$