Question

The following table shows frequencies for red-green colour blindness, where M rep-resents “person is male”, and C represents “person is colour-blind.” Use this table tofind the following probabilities.

	M	M'	Totals
C	0.035	0.004	0.039
C'	0.452	0.509	0.961
Totals	0.487	0.513	1.000

(a)(1 point) P (M )

(b)(1 point)P (C)

(c)(1 point) P (M ∩ C)

(d)(1 point) P (M ∪ C)

(e)(1 point) P (M |C)

(f)(1 point) P (C|M )

(g)(1 point) P (M′|C)

(h)(2 points) Are the events C and Mdescribed above dependent? Give quantita-tive justification.

Answer 1

	M	M'	Totals
C	0.035	0.004	0.039
C'	0.452	0.509	0.961
Totals	0.487	0.513	1.000

(a) P(M) = 0.487

(b) P(C) = 0.039

(c) P(M C) = 0.035

(d) P(M C) = P(M) +P(C) - P(M C)

= 0.487 + 0.039 -0.035 = 0.491

(e) P(M | C) = P(M C)/ P(C) = 0.035/0.039 = 0.8974

(f) P (C | M) = P(M C)/ P(M) = 0.035/0.487 = 0.0719

(g) P (M′|C) = 1- P(M|C) = 1-0.8974 = 0.1026

(h) Yes, the events C and M are dependent.

As P(C M) is not equal to P(M)*P(C). so they are not independent. and so thay are dependent.