Question

A report describes results of a survey of nearly 2,000 college faculty. The report indicates the following.

• 30.5% reported that they use Twitter and 69.5% said that they did not use Twitter.
• Of those who use Twitter, 39.8% said they sometimes use Twitter to communicate with students.
• Of those who use Twitter, 26.5% said that they sometimes use Twitter as a learning tool in the classroom.

Consider the chance experiment that selects one of the study participants at random and define the following events.

• T = event that selected faculty member uses Twitter
• C = event that selected faculty member sometimes uses Twitter to communicate with students
• L = event that selected faculty member sometimes uses Twitter as a learning tool in the classroom

(a)

Two of the percentages given in the problem specify unconditional probabilities, and the other two percentages specify conditional probabilities. Which are conditional probabilities?

69.5% said that they did not use Twitter.30.5% reported that they use TwitterOf those who use Twitter, 26.5% said that they sometimes use Twitter as a learning tool in the classroom.Of those who use Twitter, 39.8% said they sometimes use Twitter to communicate with students.

(b)

Use the given information to determine the following probabilities. (Round your answers to three decimal places.)

(i)

P(T )

(ii)

P(T ^C)

(iii)

P(C|T )

(iv)

P(L|T )

(c)

Complete the following hypothetical 1,000 table using the given probabilities. (Round your answers to the nearest integer.)

	Uses Twitter (T)	Does Not Use Twitter (not T)	Total
Uses Twitter to Communicate with Students (C)
Does Not Use Twitter to Communicate with Students (not C)
Total			1,000

Use the information in the table to calculate

P(C),

the probability that the selected study participant sometimes uses Twitter to communicate with students.

(d)

Complete the following hypothetical 1,000 table using the given probabilities. (Round your answers to the nearest integer.)

	Uses Twitter (T)	Does Not Use Twitter (not T)	Total
Uses Twitter as a Learning Tool in Classroom (L)
Does Not Use Twitter as a Learning Tool in Classroom (not L)
Total			1,000

Use the information in the table to calculate

P(L),

the probability that the selected study participant sometimes uses Twitter as a learning tool in the classroom.

Answer 1

ANSWER a:

The two conditional probabilities are-

• Of those who use Twitter, 39.8% said they sometimes use Twitter to communicate with students.
• Of those who use Twitter, 26.5% said that they sometimes use Twitter as a learning tool in the classroom.

As, the students have to first use Twitter in order to communicate or use it as a learning tool.

and, The two unconditional probabilities are-

• 30.5% reported that they use Twitter
• 69.5% said that they did not use Twitter.

ANSWER b:

Given,

• T = event that selected faculty member uses Twitter
• C = event that selected faculty member sometimes uses Twitter to communicate with students
• L = event that selected faculty member sometimes uses Twitter as a learning tool in the classroom

i. P(T)= 0.305

ii. P(T C) = P(C|T) P(T) = 0.3980.305 = 0.121 ( upto 3 decimal places)

iii. P(C|T) = 0.398 ( from the question)

iv. P(L|T)= 0.265 (from the question)

ANSWER c:

By taking the above probabilities the hypothetical 1000 table is given as-

	Uses Twitter (T)	Does not use Twitter (not T)	Total
Uses Twitter to Communicate with Students (C)	121	0	121
Does Not Use Twitter to Communicate with Students (not C)	184	695	879
Total	305	695	1000

Therefore,

P(C),the probability that the selected study participant sometimes uses Twitter to

communicate with students= 121/1000=0.121

ANSWER d:

By taking the above probabilities the hypothetical 1000 table is given as-

	Uses Twitter(T)	Does not use Twitter(not T)	Total
Uses Twitter as Learning Tool in classroom(L)	81	00	81
Does not use Twitter as a Learning tool in classroom(not L)	224	695	919
Total	305	695	1000

Therefore,

P(L),the probability that the selected study participant sometimes uses Twitter

as a learning tool in the classroom= 81/1000=0.081