Question

Please find the question at the following link:

bit.ly/2s4jgE5

Thanks.

Answer 1

Problem 8(a) FALSE

So, it is not true.

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Problem 8(b) FALSE

So, it is not true

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Problem 9

Given, are rational numbers.

So, let where   are integers and

Now,

Since are integers, so are the numbers .

Since , so is

Thus, is a rational number.

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Problem 10(a)

One officer is selected at random from each group.

Group has officers of which are males.

So, probability that one officer selected at random from this group is male

Group has officers of which are males.

So, probability that one officer selected at random from this group is male

Combining these two independent events, we obatin

Probability that the two officers are male

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Problem 10(b)

One male and one female can be from either of the two groups.

So, there are two cases:

Case(1): Male from group A and female from group B, or

Case(2): Male from group B and female from group A

Probability that one officer selected at random from group A is male

Probability that one officer selected at random from group A is female

Probability that one officer selected at random from group B is male

Probability that one officer selected at random from group B is female

Case(1): Probability

Case(2): Probability

Combining these two disjoint cases, we obatin

Probability that the one officer is male and one is female

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Problem 10(c)

Let be the event that one officer selected at random from group A is male.

Let be the event that one officer selected at random from group B is male.

We know from previous calculations that,

Also, from Problem 10(a), we know that

Now, we want to find

So,

We could have found the same answer if we argued that event is independent of event

i.e., whether an officer selected from group B is male is completely independent of the selected officer in group A.