# Not Mutually Exclusive Events

Discussion in 'Probability and Statistics' started by nycmathguy, Jul 10, 2022.

1. ### nycmathguy

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Seeking two word problems that will allow me to apply the formula P(A n B) = P(A) + P(B) - P(A U B).

nycmathguy, Jul 10, 2022

2. ### MathLover1

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how is that possible "eat dinner" and "dive" in the same time?

1. What is the probability of getting a diamond or a queen from a well-shuffled deck of 52 cards?
Solution:
Let X be the event of ‘getting a diamond’ and,
Y be the event of ‘getting a queen’
We know that, in a well-shuffled deck of 52 cards there are 13 diamonds and 4 queens.

Therefore, probability of getting a diamond from well-shuffled deck of 52 cards = P(X) = 13/52 = 1/4

The probability of getting a queen from well-shuffled deck of 52 cards = P(Y) = 4/52 = 1/13

Similarly, the probability of getting a diamond queen from well-shuffled deck of 52 cards = P(X ∩ Y) = 1/52

According to the definition of mutually non-exclusive we know that, drawing of a well-shuffled deck of 52 cards ‘getting a diamond’ and ‘getting a queen’ are known as mutually non-exclusive events.

We have to find out Probability of X union Y.

So according to the addition theorem for mutually non- exclusive events, we get;

P(X ∪ Y) = P(X) + P(Y) - P(X ∩ Y)

Therefore, P(X U Y)

= 1/4 + 1/13 - 1/52

= (13 + 4 - 1)/52

= 16/52

= 4/13

Hence, probability of getting a diamond or a queen from a well-shuffled deck of 52 cards = 4/13.

2. A lottery box contains 50 lottery tickets numbered 1 to 50. If a lottery ticket is drawn at random, what is the probability that the number drawn is a multiple of 3 or 5?

follow the steps in 1. and solve

MathLover1, Jul 10, 2022
nycmathguy likes this.

3. ### nycmathguy

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Good information. I will solve number 2 when time allows. No more math today. Brain dead.