Question

Suppose that a bag contains 3 red chips and 7 white chips. Suppose that chips are drawn from the bag with replacement, i.e. the chips are returned to the bag and shuffled before the next chip is selected. Identify the correct statement.

	a.	If ten chips are selected then seven will definitely be white.
	b.	If seven consecutive white chips are selected then the next chip will definitely be red.
	c.	If many chips are selected then, in the long run, approximately 30% will be red.
	d.	If ten chips are selected then three will definitely be red.

An activity consists of choosing a student at random and recording their gender and their grade level. Which one of the following gives the sample space for the activity?

	a.	S = { M, F, Fresh., Soph., Jun., Sen. }
	b.	S = { (M, Fresh.), (M, Soph.), (M, Jun.), (M, Sen.), (F, Fresh.), (F, Soph.), (F, Jun.), (F, Sen.) }
	c.	S = { M, F }
	d.	S = { Fresh., Soph., Jun., Sen. }

1. Let     A = {a, e, k, m} B = {b, g, h, r, w} C = {d, k n}     D = {m, r}.

   Which of the following pairs of sets are disjoint? Choose all that apply.

   	a.	A and B are disjoint.
   	b.	B and C are disjoint.
   	c.	A and C are disjoint.
   	d.	C and D are disjoint.
   	e.	A and D are disjoint.
   	f.	B and D are disjoint.
   	a.	0.65
   	b.	0.40
   	c.	0.90
   	d.	0.15

2. At a popular coffee shop one Saturday morning 60% of the customers purchase coffee, 30% purchase a bagel, and 25% purchase both. Suppose that a customer is selected at random. What is the probability that the customer purchases a coffee or a bagel?

   	a.	0.65
   	b.	0.40
   	c.	0.90
   	d.	0.15

   Which one of the following does not describe an activity that results in independent outcomes?

   	a.	Drawing five cards one-at-a-time, with replacement, from a well-shuffled deck.
   	b.	Picking four M&Ms from a bowl and eating each one before the next pick.
   	c.	Rolling a six-sided die two times.
   	d.	Flipping a coin three times.

Answer 1

Suppose that a bag contains 3 red chips and 7 white chips. Suppose that chips are drawn from the bag with replacement, i.e. the chips are returned to the bag and shuffled before the next chip is selected. Identify the correct statement.

The bag contains 30% of red chips and 70% of white chips, and the picking is with replacement

Hence the correct answer is:

c. If many chips are selected then, in the long run, approximately 30% will be red.

An activity consists of choosing a student at random and recording their gender and their grade level. Which one of the following gives the sample space for the activity?

Te gender and the grades of the students are getting recorded ( they are not selected on that basis )

Hence the correct answer is:

d. S = { Fresh., Soph., Jun., Sen. }

Let     A = {a, e, k, m} B = {b, g, h, r, w} C = {d, k n}     D = {m, r}.

Which of the following pairs of sets are disjoint? Choose all that apply.

Events are disjoint if they have nothing in common

A and B has nothing in common

A and C has k in common

A and D  has m in common

B and C has nothing in common

B and D  has r in common

C and D has nothing in common

Hence the correct answer is:

a. A and B are disjoint.

b. B and C are disjoint.

d. C and D are disjoint.

At a popular coffee shop one Saturday morning 60% of the customers purchase coffee, 30% purchase a bagel, and 25% purchase both. Suppose that a customer is selected at random. What is the probability that the customer purchases a coffee or a bagel?

P[ the customer purchases a coffee or a bagel ] = P[ customers purchase coffee ] + P[ customers purchase bagel ] - P[ customers purchase both ]

P[ the customer purchases a coffee or a bagel ] = 60% + 30% - 25%

P[ the customer purchases a coffee or a bagel ] = 65%

P[ the customer purchases a coffee or a bagel ] = 0.65

Hence the correct answer is:

a. 0.65

Which one of the following does not describe an activity that results in independent outcomes?

The outcomes are independent if draw of one do alter the Probability of drawing of another

Hence the correct answer is:

b. Picking four M&Ms from a bowl and eating each one before the next pick.