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Help me solve this question. They are from straighterline.com intro to statistics course for Liberty University
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1. Two methods, A and B, are available for teaching a certain industrial skill. There is a 75% chance of
successfully learning the skill if method A is used, and a 95% chance of success if method B is used.
However, method B is substantially more expensive and is therefore used only 20% of the time
(method A is used the other 80% of the time).
The following notations are suggested:
A—method A is used.
B—method B is used.
L—the skill was Learned successfully.
Which of the following is the correct representation of the information that is provided to us? P(A)
= .80, P(B) = .20, P(A | L) = .75, P(B | L) = .95
P(A) = .80, P(B) = .20, P(A and L) = .75, P(B and L) = .95
P(A) = .80, P(B) = .20, P(L | A) = .75, P(L | B) = .95
P(A | L) = .80, P(B | L) = .20, P(L | A) = .75, P(L | B) = .95
P(A and L) = .80, P(B and L) = .20, P(L | A) = .75, P(L | B) = .95
2. 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:
(i)
31% of all Dalmatians have blue eyes.
(ii)
(ii) 38% of all Dalmatians are deaf.
(iii)
(iii) 42% of blue-eyed Dalmatians are deaf.
What is the probability that a randomly chosen Dalmatian is blue-eyed and deaf?
3. A and B, 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% 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). draw probability tree.
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