Question

Jonathan has a bag that co rains exactly one red marble (r), one yellow marble (y) and one green marble (g). He chooses a marble form the bag without looking. Without replaces the marble he chooses a second marble from the bag without looking. Which outcomes would be included in the sample space for Jonathan's experiment?

Answer 1

Correct choices are 2, 4 and 5

Explanation:

Jonathon chooses a marble from the bag without looking: it can be red (r) marble, (y) yellow marble or (g) green marble. Then without replacing chosen marble, he chooses a second marble from the bag without looking.

If the first marble was (r), then the second can be (y) or (g).

If the first marble was (y), then the second can be (r) or (g).

the first marble was (g), then the second can be (y) or (r).

There are 6 possible outcomes:

ry, rg, yr, yg, gy, gr.

Answer 2

Answer: The first outcome shall be 0.33 or 33%.

The second outcome would be 0.5 or 50%

Step-by-step explanation: The bag contains exactly one yellow, one red and one green marble. So when he draws the first marble the sample space shall be the total possible outcomes, which is three, since he has three (3) marbles altogether. When he draws the first time without looking, all three marbles have an equal probability of being picked which can be derived thus;

P(Red) = Number of required possibilities/Number of all possibilities

P(Red) = 1/3

P(Red) = 0.33

Note that there is only one marble of each color which means P(Yellow) and P(Green) is also 0.33 respectively.

After choosing the first marble, without replacing the first one he now chooses another marble. The sample size would have reduced to 2 (since one marble has been drawn). Hence, the outcome when he draw a second marble can be calculated as follows;

P(Red) = Number of required outcomes/Number of possible outcomes

P(Red) = 1/2

P(Red) = 0.5