Question

Consider an experiment with a standard 52-deck from which one card is randomly selected and not...

Consider an experiment with a standard 52-deck from which one card is randomly selected and not replaced. Then a second card is randomly selected. Define the following events:

Event A = The first card is a heart

Event B = The second card is a heart

a. Are these two events mutually exclusive? Why or Why not?

b. Are these two events independent? Why or why not?

Math   Statistics-And-Probability   
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Answer #1

Event A = The first card is a heart

Event B = The second card is a heart

a) Two events are mutually exclusive , when both the events cannot happen together Or we can said that both of them are disjoint

Here Event A and B are not mutually exclusive , As they are not disjoint, Happening of one can occur with the other.

That means we can draw two heart consecutively without replacement

b) Two events are independent when occuring of one does not effect the occuring of the other.

Here as we draw the cards withuot replacement, So No two events are not not independent . As occuring of Event A effects Event B.

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