1. A sample survey chooses a sample of households and measures their annual inco

Question

1. A sample survey chooses a sample of households and measures their annual income and their savings. Interesting events: A- the household chosen has income of at least $100,000 8- the household chosen has at least $50,000 in savings PA)-0.0 P(B)-02 [Circle the Correct Answer] Do you expect that events A and B are independent or dependent? a. b. (Circle the Correct Answer] Do you expect that events A and B are mutually exclusive or not mutually exclusive? c We want to find the probability that a household either has income of at least $100,000 or has a savings of at least $50,000. Explain what additional information is needed to find this probability. that a household has income at least $100,000 and has savings of at least $50,000. We want to find the probability Explain what additional information is needed to find this probability d.

Explanation / Answer

a) Answer: Dependent

To decide an event is independent of other, we first need to know whether occurring an event is independent of other or not.

Occurring/Not-occurring of an event should not affect other event's Occurring/Not-occurring probability.

Means

I]

i) P(A/B) = P(A) and ii) P(B/A) = P(B) or II] P(A intersection B) = P(A) x P(B)

If any one above not holds means they are dependent.

Here in our problem,

A = income having at least 1 Lakh

B = savings of at least 50,000

Here P(A/B) may not equal P(A)

Because there can be some households which are having income of at least 1 Lakh and not saving at least 50,000. It is possible. This reason will reduce P(A/B) value than P(A). So, both may not be equal always.

So, result is dependent.

b) Answer: Not mutually exclusive

To decide this, we need to know whether one event occurrence is completely restricting to happen other event and viceversa. Then we can say both are mutually exclusive events.

P(A intersection B) = 0

There can be some households which are having income of at least 1 Lakh and saving 50,000 as well. It is possible. So, both are mutually not exclusive events.

c) P(A Union B) = ?

= P(A) + P(B) + P(A intersection B)

All the above cases of my answers are some possible reasons or expectations. But not sure answers. Because there is no enough information to find exactly. They just gave P(A) and P(B). With these values we cannot surely tell they are mutually exclusive or not(P(A intersection B) = 0 ?).

Means we want that whether these events are

i) independent or dependent

ii) exclusive or not exclusive

With above confirmation we can find P(A intersection B)

d) P(A intersection B) = ?

For this also it is enough to know the above extra info(i and ii).

Ping me if any help need to understand

Thumbs up, please?

Thank you.

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