Question

The chef at a school cafeteria asked students whether they like peas. for the students surveyed, are liking peas and being male independent or dependent events? justify your answer

A.) Dependent;

P(likes peas) =39%

P(male/likes peas) =54%

since these probabilities are not equal, the events are dependent.


B.) Dependent;

P(likes peas) =39%

P(likes peas/male) = 42%

since these probabilities are not equal, the events are dependent.


C.) Independent;

P(likes peas) =39%

P(likes peas/male) =42%

since these probabilities are not equal, the events are independent.


D.) Independent;

P(likes peas) =39%

P(male/likes peas) =54%

since these probabilities are not equal, these events are independent.

Answer 1

B

Explanation:

In the Dependent case the following relation must be satisfied:

p(a|b) = p(a∩b)/p(b)

Or, in terms of this problem:

p(like peas|male) = p(like peas∩male)/p(male)

The probabilities of this events are:

p(like peas|male) = 42/100 = 42%

p(like peas∩male) = 42/200 = 21%

p(male) = 100/200 = 50%

Therefore, the events are dependent

In the Independent case the following relation must be satisfied:

p(a|b) = p(a)

or

p(like peas|male) = p(like peas)

p(like peas) = 78/200 = 39%

The equation is not satisfied.

Answer 2

Option B

Explanation:

Given:

total No. of students liking peas= 78

total no. of male students= 100

total number of students= 200

no. of male students liking peas= 42

Now we need to find are liking peas and being male independent or dependent events

P(likes peas)= 78/00

=0.39

=39%

P(likes peas/male) = 42/100

= 42%

as the two probabilities are not equal the two events are dependent.

Hence option B is correct: Dependent;

since these probabilities are not equal, the events are dependent!