Question

1. Suppose we have an urn filled with different color marbles. There are 3 red marbles, 4 green marbles, 2 blue marbles, and 5 yellow marbles. Suppose that all of the marbles are numbered; the red marbles are numbered 1 through 3, the blue marbles are numbered 1 and 2, the green marbles are numbered 1 through 4, and the yellow marbles are numbered 1 through 5. Suppose that we conduct a probability experiment where we draw a single marble from the urn. (a) Identify the sample space (b) What is the probability of drawing a red marble? (c) What is the probability of drawing a marble with the number 2 on it? (d) Is the event that we draw a blue marble mutually exclusive from the event that we draw a 2? (e) Is the event that we draw a blue marble independent from the event that we draw a 2? (f) What is the probability that we draw a yellow marble that has a number less than or equal to 2? (g) What is the probability that we draw a yellow marble or a marble that has a number less than or equal to 2?

          1. Suppose we have an urn filled with different color marbles.
There are 3 red marbles, 4 green marbles, 2 blue marbles, and 5
yellow marbles. Suppose that all of the marbles are numbered; the
red marbles are numbered 1 through 3, the blue marbles are numbered
1 and 2, the green marbles are numbered 1 through 4, and the yellow
marbles are numbered 1 through 5. Suppose that we conduct a
probability experiment where we draw a single marble from the urn.
(a) Identify the sample space (b) What is the probability of
drawing a red marble? (c) What is the probability of drawing a
marble with the number 2 on it? (d) Is the event that we draw a
blue marble mutually exclusive from the event that we draw a 2? (e)
Is the event that we draw a blue marble independent from the event
that we draw a 2? (f) What is the probability that we draw a yellow
marble that has a number less than or equal to 2? (g) What is the
probability that we draw a yellow marble or a marble that has a
number less than or equal to 2?

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Added by Tara C.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

05/05/2023

Step 1

We can represent each outcome as a pair (color, number). The sample space is: S = {(R,1), (R,2), (R,3), (G,1), (G,2), (G,3), (G,4), (B,1), (B,2), (Y,1), (Y,2), (Y,3), (Y,4), (Y,5)} Show more…

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1. Suppose we have an urn filled with different color marbles. There are 3 red marbles, 4 green marbles, 2 blue marbles, and 5 yellow marbles. Suppose that all of the marbles are numbered; the red marbles are numbered 1 through 3, the blue marbles are numbered 1 and 2, the green marbles are numbered 1 through 4, and the yellow marbles are numbered 1 through 5. Suppose that we conduct a probability experiment where we draw a single marble from the urn. (a) Identify the sample space (b) What is the probability of drawing a red marble? (c) What is the probability of drawing a marble with the number 2 on it? (d) Is the event that we draw a blue marble mutually exclusive from the event that we draw a 2? (e) Is the event that we draw a blue marble independent from the event that we draw a 2? (f) What is the probability that we draw a yellow marble that has a number less than or equal to 2? (g) What is the probability that we draw a yellow marble or a marble that has a number less than or equal to 2?

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Transcript

00:01 Hello, let's have a look on the question.

00:01 So here we have the sample space of red, green, blue and yellow marbles and these are the numbers.

00:07 Now the total number of number of marbles marked 1 is equal to 4.

00:17 Number of marbles marked 2 is equal to 4.

00:22 Number of marbles marked 3 is equal to 3 and the number of marbles that are marked 4 is equal to 2.

00:33 The number of marbles that are marked 5 is equal to 1.

00:38 Now here we need to find out this is for the first part we can say this is the answer for the first part that is we only need to find out the sample space.

00:46 Moving on for the second part we need to find out the probability of for the b part we need to find out the probability of drawing red marble.

00:57 Red marble so this will be equal to total number of total number of red divided by total marble this will be equal to we have three red marbles and total we have 14 marbles.

01:18 This will be the probability for drawing a red marble.

01:22 Moving on we have for the c part the probability of drawing a marble with a number 2 on it.

01:30 Number 2 on it.

01:33 This will be equal to since the number of marbles that are marked 2 is equal to 4.

01:38 So 4 divided by 14 will be equal to 2 divided by 7.

01:42 This is the probability for number 2 marked on a marble.

01:45 Moving on to the d part we need to answer the mutually exclusive.

01:50 So we can so here we can say that no as the mutually exclusive events if occurrence one prevents the occurrence of other in mutually exclusive one event prevents the occurrence of other one occurrence of event 2.

02:19 So here we can say blue ball is not numbered as 2.

02:23 So the both events can happen together as blue ball is not numbered 2.

02:34 So both can happen together.

02:38 Both events can happen together...

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