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3 years ago

7

I WILL GIVE AN EXTRA 50 POINTS TO WHOEVER GETS THESE 2 QUESTIONS RIGHT

1 answer:

nikdorinn [45]3 years ago

4 0

Answer:

See below for answers and explanations

Step-by-step explanation:

<u>Problem 1:</u>

A standard deck of cards contains 52 cards, consisting of 13 spades. If you select only one randomly, the probability of that occurring would be 13/52 or 1/4. Since there are only 26 red cards in a standard deck, then the probability of selecting a red card would be 26/52 or 1/2. Because the two events are independent of each other, their probabilities are multiplied. Therefore, the probability of selecting a spade, and then replacing it in hopes of drawing a red card is (1/2)(1/4) = 1/8.

<u>Problem 2:</u>

We are selecting a spade and then another spade while NOT replacing the first spade (remember that these events are independent of each other also). This means that the total card count will change by picking up the second card. Therefore, the probability of selecting a spade, followed by another spade, is (13/52)(12/51) = 156/2652 = 1/17.

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Dustin has a bag of marbles with 4 blue marbles, 4 white marbles, and 3 red marbles.

diamong [38]

Answer:

A.

$\dfrac{6}{55}$

B.

$\dfrac{6}{55}$

C.

$\dfrac{4}{165}$

Step-by-step explanation:

Dustin has a bag of marbles with 4 blue marbles, 4 white marbles, and 3 red marbles. There are 11 marbles in total.

A. The probability that the first marble drawn is blue marble is

$\dfrac{4}{11},$

the probability that the second marble drawn is red marble is

$\dfrac{3}{10}$

The probability that the first marble drawn is blue and the second is red is

$\dfrac{4}{11}\cdot \dfrac{3}{10}=\dfrac{12}{110}=\dfrac{6}{55}$

B. The probability that the first marble drawn is red marble is

$\dfrac{3}{11},$

the probability that the second marble drawn is white marble is

$\dfrac{4}{10}$

The probability that the first marble drawn is red and the second is white is

$\dfrac{3}{11}\cdot \dfrac{4}{10}=\dfrac{12}{110}=\dfrac{6}{55}$

C. The probability that the first marble drawn is blue marble is

$\dfrac{4}{11},$

the probability that the second marble drawn is blue marble is

$\dfrac{3}{10},$

the probability that the third marble drawn is blue marble is

$\dfrac{2}{9},$

The probability that the first, second and third marbles drawn are blue is

$\dfrac{4}{11}\cdot \dfrac{3}{10}\cdot \dfrac{2}{9}=\dfrac{24}{990}=\dfrac{4}{165}$

8 0

3 years ago