Find the probability for the following problems
The following three problems (i.e., problems 1-3) refer to the following information:
assume a basketball team had a season of games with the following characteristics:
- 60% of all the games were at-home games. Denote this by H (the remaining were away games).
25% of all games were wins. Indicate this by W (the remaining were losses).
- 20% of all games were at-home wins.
1. Of the at-home games, we are interested in finding what proportion were wins. In order to figure this out, we need to find:
a.P (H)
b.P (W)
c.P (H and W)
d.P (H | W)
e.P (W | H)
2. Of the at-home games, what proportion of games were wins? (Note: Some answers are rounded to 2 decimal places.)
a..12
b..15
c..20
d..33
e..42
3. If the team won a game, how likely is it that this was a home game? (Note: Some answers are rounded to 2 decimal places.)
i. .05
ii. .12
iii..15
iv..42
v..80
4. Let A and B be two independent events. If P(A) = .5, what can you say about P(A | B)?
a.Cannot find it since P (B) is not known.
b.Cannot find it since P (A and B) is not known.
c.Cannot find it since both P (B) and P (A and B) are not known.
d.It is equal to .5.
e.It is equal to .25.
The next two problems (i.e., problems 5 and 6) refer to the following information: Dogs are inbred for such desirable characteristics as blue eye color; but an unfortunate by-product of such inbreeding can be the emergence of characteristics such as deafness. A 1992 study of Dalmatians (by Strain and others, as reported in The Dalmatians Dilemma) found the following:
a.31 percent of all Dalmatians have blue eyes.
b.38 percent of all Dalmatians are deaf.
c.42 percent of blue-eyed Dalmatians are deaf.
5. Based on the results of this study is "having blue eyes" independent of "being deaf"?
a.No, since .31 * .38 is not equal to to .42.
b.No, since .38 is not equal to .42.
c.No, since .31 is not equal to .42.
d.Yes, since .31 * .38 is not equal to .42.
e.Yes, since .38 is not equal to .42.
6. What is the possibility that a randomly chosen Dalmatian is blue-eyed and deaf?
a..31 * .38 = .1178
b..31 * .42 = .1302
c..38 * .42 = .1596
d..31 / .38 = .8158
e..31 / .42 = .7381
f..38 / .42 = .9048
The following 4 problems (i.e., problems 7-10) refer to the following information:
Two methods, A and B, are available for teaching a certain industrial skill. There is an 80% chance of successfully learning the skill if method A is used and a 95 percent chance of success if method B is used. However, method B is substantially more expensive and is therefore used only 25% of the time (method A is used the other 75% of the time). The following notations are suggested:
a.A - method A is used
b.B - method B is used
c.L - skill was learned successfully
7. Which of the following is the right representation of the information that is provided to us?
a.P(A)= .75, P(B) = .25, P(L |a) =. 80, P(L | B) = .95
b.P(A) = .75, P(B) = .25, P(A | L) = .80, P(B | L) = .95
c.P(A) = .75, P(B) = .25, P(A and L) = .80, P(B and L) = .95
d.P(A | L) = .75, P(B | L) = .25, P(L |a) = .80, P(L | B) = .95
e.P(A and L) = .75, P(B and L) = .25, P(L |a) = .80, P(L | B) = .95