In August 2017, the Annenberg Public Policy Center asked the equivalent of a sim
ID: 3277354 • Letter: I
Question
In August 2017, the Annenberg Public Policy Center asked the equivalent of a simple random sample of 705 U.S. adults the following: “Would you mind naming any of (the three branches of government)?” The equivalent results are summarized below.
- 183 named all three branches
- 92 named two of the three branches
- 190 named one branch
- 233 could not name any branches
- 7 refused to answer
Suppose five of the 705 adults are picked at random (without replacement) for more in-depth interviews. What is the chance that everyone in the sample will be able to name all three branches of government?
A. 0.113%
B. 1.13%
C. 0.00113%
D. 22.1%
E. 77.9%
A. 0.113%
B. 1.13%
C. 0.00113%
D. 22.1%
E. 77.9%
Explanation / Answer
ans . P(all 5 people naming all 3 branches )
P(prob of first person naming all the branches )*P(prob of second person naming all the branches )*P(prob of third person naming all the branches )*P(prob of fourth person naming all the branches )*P(prob of fifth person naming all the branches )
=(183/705)*(182/704)*(181/703)*(180/702)*(179/701)
=0.001131 or 0.113% A