I am trying to get input on number 4... 1. The 1980 U.S. population, broken down

Question

I am trying to get input on number 4...

1. The 1980 U.S. population, broken down by region and attitude to legalization of marijuana, roughly turned out as follows In Favor 7.8% 18.2% Opposed (O 22.2% 51.8% All except East AE Is F independent of E? 2. Two dice are thrown and we are interested in the following events E: first die is 5 F: Total is 7 G: Total is 10 Is the following a correct verbal conclusion? If not, correct it. "If I am going to bet on whether the dice show 7, it will help (change the chances) to peek at the first die to see whether it is a 5, if I am going to bet on whether the dice show 10, a peek won't help." 3. At an electronics plant, it is known from past experience that the probability is 0.84 that a new worker who has attended the company's training program will meet the production quota, and that the corresponding probability is 0.49 for a new worker who has not attended the company's training program. If 70% of all new workers attend the training program, what is the probability that a new worker will meet the production quota? 4. If E and F are two mutually exclusive events, what can be said about their independence?

Explanation / Answer

Question 4:

You dont need an input for this, we just have to prove the given statement using examples.

Here we are given that the 2 events E and F are mutually exclusive events. This means they cannot happen together. Now assuming that E and F are 2 events with some particular probability of occurence, then in case they are mutually exclusive, P(E and F) = 0 because they both cannot happen together if they are mutually exclusive.

And as we know that P(E) and P(F) are probable events, therefore P(E)P(F) would not be equal to 0. Therefore

P(E and F) is not equal to P(E)P(F) and therefore the 2 events are not independent.

Therefore if two events are mutually exclusive events, it is not necessary that they would also be independent events.

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