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Flashcards: Probability

A card is drawn at random from a standard deck of 52 cards (the joker is not included), and its rank and suit are recorded.

Which of the following changes both the probability of drawing a black card and that of drawing an ace?

1) Replacing the ace of spades with the joker

2) Adding the joker

3) Removing the ace of spades

(2) and (3) only

(1) only

(1) and (3) only

(1), (2), and (3)

(1) and (2) only

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Flashcards: Probability

A card is drawn at random from a standard deck of 52 cards (the joker is not included), and its rank and suit are recorded.

Which of the following changes both the probability of drawing a black card and that of drawing an ace?

1) Replacing the ace of spades with the joker

2) Adding the joker

3) Removing the ace of spades

(2) and (3) only

(1) only

(1) and (3) only

(1), (2), and (3)

(1) and (2) only

Report an Error Copyright Notice

Flashcards: Probability

A card is drawn at random from a standard deck of 52 cards (the joker is not included), and its rank and suit are recorded.

Which of the following changes both the probability of drawing a black card and that of drawing an ace?

1) Replacing the ace of spades with the joker

2) Adding the joker

3) Removing the ace of spades

Your answer:

(2) and (3) only

Your answer:

(1) only

Your answer:

(1) and (3) only

Your answer:

(1) and (2) only

Correct answer:

(1), (2), and (3)

Explanation:

If a card is drawn at random from a standard deck of 52, the probability of drawing one of the 26 black cards is $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ ; the probability of drawing an ace is $\frac{1}{13}$ $\displaystyle \frac{1}{13}$ . Now, examine each of the three scenarios.

(1) If the ace of spades is replaced with the joker, this leaves 25 black cards and 3 aces out of a total of 52 cards. The probability of drawing one of the 25 black cards is $\frac{25}{52}$ $\displaystyle \frac{25}{52}$ ; the probability of drawing an ace is $\frac{3}{52}$ $\displaystyle \frac{3}{52}$ .

(2) If the joker is added, there are still 26 black cards and 4 aces, but the deck now has 53 cards. The probability of drawing one of the 25 black cards is $\frac{26}{53}$ $\displaystyle \frac{26}{53}$ ; the probability of drawing an ace is $\frac{4}{53}$ $\displaystyle \frac{4}{53}$ .

(3) If the ace of spades is removed, this leaves 25 black cards and 3 aces out of a total of 51 cards. The probability of drawing one of the 25 black cards is $\frac{25}{51}$ $\displaystyle \frac{25}{51}$ ; the probability of drawing an ace is $\frac{3}{51} = \frac{1}{17}$ $\displaystyle \frac{3}{51} = \frac{1}{17}$ .

In all three cases, both probabilities have changed.

Flashcards: Probability

The odds in favor of an event occurring are 17 to 4. To the nearest hundredth, what is the probability of the event happening?

0.81 $\displaystyle 0.81$

0.71 $\displaystyle 0.71$

0.86 $\displaystyle 0.86$

0.76 $\displaystyle 0.76$

0.91 $\displaystyle 0.91$

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Flashcards: Probability

The odds in favor of an event occurring are 17 to 4. To the nearest hundredth, what is the probability of the event happening?

Your answer:

0.71 $\displaystyle 0.71$

Your answer:

0.86 $\displaystyle 0.86$

Your answer:

0.76 $\displaystyle 0.76$

Your answer:

0.91 $\displaystyle 0.91$

Correct answer:

0.81 $\displaystyle 0.81$

Explanation:

If the odds in favor of an event are $\displaystyle a$ to $\displaystyle b$ , the probability of that event is $\frac{a}{a+b}$ $\displaystyle \frac{a}{a+b}$ . Setting a= 17 $\displaystyle a= 17$ and b = 4 $\displaystyle b = 4$ , the probability of the event is

$\frac{17}{17+4} = \frac{17}{21} \approx 0.81$ $\displaystyle \frac{17}{17+4} = \frac{17}{21} \approx 0.81$ .

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Flashcards: Probability

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Flashcards: Probability

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Flashcards: Probability

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