**7)** Hi this is Asmita! I am a Student Success Coach and will be explaining some practice problems from the MA121 Introduction to Statistics course. Today we will review an assigned problem from Unit 2. In the “Homework Assessment” you were asked to solve this problem:

In the situation of Exercise 3, list the outcomes that comprise each of the following events.

a.No yellow marble is drawn.

b.The two marbles drawn have the same color.

c.At least one marble of each color is drawn.

We will use the concept of a sample space and a subset of the sample space to list the all possible outcomes for events.

We will approach this problem as follows:

1.Write the sample space by referring of Exercise 3.

2.List out the all appropriate outcomes from the sample space which are required for given events.

3.Write down the outcomes in set notation.

By referring Exercise 3, the sample space for randomly drawing two marbles with replacement in succession from a box containing 8 red, 8 yellow, and 8 green marbles is

S= {rr, ry, rg, yr, yy, yg, gr, gy, gg}

**a.**

**Step 1:** Define an event.

Define A: No yellow marble is drawn.

**Step 2:** Write the all outcomes for “no yellow marble is drawn”.

No yellow marble is drawn means neither yellow marble is selected in first draw nor in second draw. So outcomes are red and red, red and green, green and red, green and green.

Therefore, the total outcomes for the event A” No yellow marble is drawn” are **‘rr’, ‘rg’, ‘gr’ and ‘gg’.**

**Step 3:** Write down the outcomes in set notation.

The outcomes for the event A are {rr, rg, gr, gg}

**b.**

**Step 1:** Define an event.

Define B: The two marbles drawn have the same color.

**Step 2:** Write the all outcomes for “The two marbles drawn have the same color”.

The two marbles drawn have the same color means in two succession draws both marbles have same color. That means both marbles are red or yellow or green.

Therefore, the total outcomes for an event B ”The two marbles drawn have the same color” are **‘rr’,’ yy’ and ‘gg’.**

**Step 3:** Write down the outcomes in set notation.

The outcomes for the event B are {rr, yy, gg}

**c.**

**Step 1:** Define an event

Define C: At least one marble of each color is drawn.

**Step 2:** Write the all outcomes for “At least one marble of each color is drawn”.

At least one marble of each color is drawn means the outcome containing three different colored marbles. As selecting only two marbles in succession with replacement, it is not possible to get outcome such that at least one marble of each color is drawn.

Therefore, there is no possible outcome for an event C and it is denoted by Ø (the “empty “ set that has no outcome ).

**Step 3:** Write down the outcomes in set notation.

Ø (the “empty” set that has no outcome)

**Conclusion:**

The outcomes for each event are

a. {rr, rg, gr, gg}

b. {rr, yy, gg}

c. Ø (The “empty” set that has no outcome)

In addition to this, I am also attaching the pdf document of the practice problem for your ready reference.

Question 7.pdf (111.6 KB)

Please let me know if you have any question on this problem, or on this topic generally. I will be here in the forum for the next hour.