Question

4.13 Are whites more likely to claim bias? A survey conducted by Barry Goldman found that of 56 white workers terminated, 29 claimed bias. Of 407 black workers terminated, 126 claimed bias. Construct a contingency table or a Venn diagram to evaluate the probabilities. If a worker is selected at random, what is the probability that he or she

a. Claimed bias?

b. is black and did not claim bias?

c. is black or claimed bias?

d. Explain the difference in the results in (b) and (c).

Answer 1

9a)

From the given data, the following Table is calculated:

	Claimed bias	Did not claim bias	Total
White	29	27	56
Black	126	281	407
Total	155	308	463

P(Claimed bias) = 155/463 = 0.3348

So,

Answer is:

0.3348

(b)
P(Black AND Did not claim bias) = 281/463 = 0.6069

So,

Answer is:

0.6069

(c)
P(Black OR Claimed bias) = P(Black) + P(Claimed bias) - P(Black AND Claimed bias)

= 407/463   + 155/463 - 126/463

= 436/463

= 0.9417

So,

Answer is:

0.9417

(d)

In (b) probability of the 2 events occurring together was derived. In (c) the probability of occurrence of either of the 2 events was derived.