Question

Barbara draws pens randomly from a box containing 5 pens of the same shape and size. There is 1 green pen, 3 red pens, and 1 blue pen. She draws 1 red pen and then another red pen without replacing the first one. Find the probability of drawing 1 red pen followed by another red pen, and show the equation used. (10 points)

Question 1 options:
Question 2 (10 points)
(07.02 MC)
Leena is arranging 3 different books in a row on a shelf. Create a sample space for the arrangement of a detective story (D), a mystery story (M), and a comic book (C). (10 points)

Question 2 options:
Question 3 (10 points)
(07.01 MC)
A box has 1 red marble, 1 blue marble, and 4 green marbles of the same shape and size. Dan draws a marble randomly from the box, replaces it, and then draws another marble randomly. What is the probability of drawing two green marbles in a row? Explain your answer. (10 points)

Question 3 options:
Question 4 (10 points)
(07.03 MC)
Chang has 2 shirts: a white one and a black one. He also has 2 pairs of pants, one blue and one tan. What is the probability, if Chang gets dressed in the dark, that he winds up wearing the white shirt and tan pants? Show your work. (10 points)

Question 4 options

Answer 1

Question 1:

In the given scenario, Barbara draws 1 red pen followed by another red pen without replacing the first one. To calculate the probability of this event, we can use the concept of conditional probability.

The probability of drawing the first red pen is 3/5 because there are 3 red pens out of a total of 5 pens in the box. After drawing the first red pen, there are now 4 pens remaining in the box, with 2 of them being red.

Therefore, the probability of drawing the second red pen, given that the first one was red, is 2/4.

To find the probability of both events occurring (drawing 1 red pen followed by another red pen), we multiply the individual probabilities:

Probability = (3/5) * (2/4) = 6/20 = 3/10

So, the probability of drawing 1 red pen followed by another red pen is 3/10.

Question 2:

The sample space for arranging the detective story (D), mystery story (M), and comic book (C) in a row would be:

{DMC, DCM, MDC, MCD, CMD, CDM}

This represents all the possible arrangements of the three books.

Question 3:

In this scenario, there are 6 marbles in the box: 1 red, 1 blue, and 4 green. Dan first draws a marble randomly from the box, replaces it, and then draws another marble randomly.

The probability of drawing a green marble on the first draw is 4/6 because there are 4 green marbles out of a total of 6 marbles in the box. Since the marble is replaced, the number of marbles remains the same for the second draw.

Therefore, the probability of drawing a green marble on the second draw, given that the first marble was green, is also 4/6.

To find the probability of drawing two green marbles in a row, we multiply the individual probabilities:

Probability = (4/6) * (4/6) = 16/36 = 4/9

So, the probability of drawing two green marbles in a row is 4/9.

Question 4:

Chang has 2 shirts (white and black) and 2 pairs of pants (blue and tan). If he gets dressed in the dark, the probability of wearing a white shirt and tan pants can be calculated.

The probability of selecting the white shirt is 1/2 because there is 1 white shirt out of a total of 2 shirts. Similarly, the probability of selecting tan pants is also 1/2.

To find the probability of wearing the white shirt and tan pants, we multiply the individual probabilities:

Probability = (1/2) * (1/2) = 1/4

So, the probability of Chang wearing a white shirt and tan pants is 1/4.