Probability Examples on Union

In this class, We discuss Probability Examples on Union.

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The reader should have prior knowledge of axioms of probability. Click Here.

Example 1:

Random Experiment: Toss two coins

The sum of values on the dice should be greater than nine.

The sum value should be either 10, 11,or 12.

Event E = {10 U 11 U 12}

The possibilities of sum = 10 are E1 = {(5,5), (6,4), (4,6)}

Sum value 11 = E2 = {(6,5), (5,6)}

Sum value 12 = E3 = {(6,6)}

All the events E1, E2, and E3 are disjoint events.

P(E) = P(E1) + P(E2) + P(E3)

P(E) = 3/36 + 2/36 + 1/36

P(E) = 6/36

Example 2:

Random experiment: Randomly select a card from a deck of cards.

Event E = {Spade or Ace}

We have total 13 spade cards

We have total four ace cards

The Ace of spade is common to both the selections.

The events are not disjoint events.

P(E1 U E2) = P(E1) + P(E2) – P(E1 ∩ E2)

P(E1 U E2) = 13/52 + 4/52 – 1/52

P(E1 U E2) = 16/52