Who can help solve this probability problem?

Question

A market research study is being conducted to determine if a product modification will be well received by the public. A total of 1,000 consumers are questioned regarding this product. The table below provides information regarding this sample.

Positive neutral Negative
Male 240 60 100
Female260 220 120
(a) What is the probability that a randomly selected male would find this change unfavorable (negative)?
(b) What is the probability that a randomly selected person would be a female who had a positive reaction?
(c) If it is known that a person had a negative reaction to the study, what is the probability that the person is male?

I'm not sure my answers
(a) 0.1 (b)0.26 (c)?

Answer 1

(a) There are 400 males of which 100 react negatively, thus we have a probability of 100/400 or .25

(b) There are 260 possible female positives of 1000 possibles, thus we have a probability of 260/1000 or .26

(c) There are 220 negatives of which 100 are male, thus we have a probability of 100/220 or 5/11

Answer 2

Let M = event that the randomly selected person is a male
F = event that the randomly selected person is a female
A = event that opinion is positive
B = event that the opinion is neutral and
C = event that the opinion is negative

Now let us write down the probability values of different events which may be needed from the data given.

P ( M ) = 400/1000 = 4/10
P ( F ) = 600/1000 = 6/10
P ( A / M ) = 240/400 = 6/10, P ( C / M ) = 100/400 = 1/4
P ( A / F ) = 260/600 = 13/30, P ( C / F ) = 120/600 = 2/10

( a ) P ( C / M ) is the probability that the randomly selcted male would find the change unfavorable = 1/4 = 0.25

( b ) P ( F / A ) is the probability that person is a female given the positive reaction

By Bayes' Rule,

P(F/A) = P(F) P(A/F) / [ P(M) P(A/M) + P(F) P(A/F) ]

= (6/10 x 13/30) / [(4/10)(6/10) + (6/10)(13/30)]

= 39/75 = 0.52

P ( M/C) = is the probability that person is a male given the negative reaction

By Bayes' Rule,

P(M/C) = P(M) P(C/M) / [ P(M) P(C/M) + P(F) P(C/F) ]

= (4/10 x 1/4) / [(4/10)(1/4) + (6/10)(2/10)]

= 5/11

Answer 3

a) 100/1000, which is 1/10, so you were right.
b)260/1000, or 26/100, or .26, so you were right.
c)First find the total number of people it could be, so the total number who had negative reactions, or 100+120=220. Of those, 100 are male, so the answer is 100/220, or 10/22, or 5/11.

Answer 4

100/400 = 1/4

600/1000 * 260/600 = 26%

100/220 = 5/11