Question

The following data were given in a study of a group of 1000 subscribers to a certain magazine. In reference to job, marital status, and education, there were
312 professionals,
470 married persons,
525 college graduates,
42 professional college graduates,
147 married college graduates,
86 married professionals,
25 married professional college graduates.
(i) Let a person be picked at random. Determine the probability that the person is married or professional or college graduate.
(ii) Explain why the numbers reported in the study must be incorrect.

Answer 1

Answer:

$(a)$  $P(M\ or\ P\ or\ C) = 1.307$

(b) See Explanation

Step-by-step explanation:

Given

$P = 312$ ---- Professionals,

$M = 470$ ----- Married persons,

$C = 525$ ---- College graduates,

$PCG = 42$  ----- Professional college graduates,

$MCG = 147$ ----- Married college graduates,

$MP = 86$  ---- Married professionals,

$MPCG = 25$ ---- Married professional college graduates

$Total =1000$

Solving (a): P(M or P or C)

This is calculated as:

$P(M\ or\ P\ or\ C) = P(M) + P(P) + P(C)$

$P(M\ or\ P\ or\ C) = \frac{n(M) + n(P) + n(C)}{Total}$

$P(M\ or\ P\ or\ C) = \frac{470 + 525 + 312}{1000}$

$P(M\ or\ P\ or\ C) = \frac{1307}{1000}$

$P(M\ or\ P\ or\ C) = 1.307$

(b) In probabilities, the probability of an event or collection of events must not exceed 1 and must not go below 0.

In (a) above, the calculated probability exceeds 1.

Because of this single reason, the collected data is incorrect