Probability of Disjoint and Overlapping Events

Which of the following shows how to determine P(diamond or face card)?

• 13/52 + 12/52 - 3/52

• 3/52 + 13/52 -12/52

• 3/52 + 12/52 - 13/52

• 1/13 + 3/52 - 1/4

If you are picking a card randomly from a deck of cards, the events of picking a jack and picking a heart are mutually exclusive.

• True

• False

Which of the following shows how to determine P(shaded number or number less than five)?

• 4/8 + 4/8 - 2/8

• 4/9 + 2/8 - 4/8

• 4/8 + 6/8 + 2/8

• 2/8 + 4/8 - 4/8

events that have no outcomes in common

• non-uniform

• disjoint

• overlapping

• contingency

• complement

What is P(A or B) if P(A) = 1/4 and P(B) = 1/2, where A and B are overlapping events and P(a and B) = 1/8?

• 1/7

• 1/12

• 5/8

• 1/2

Which formula do you use when two events are overlapping events?

• P(A or B) = P(A) + P(B)

• P(A or B) = P(A) + P(B) - P(both)

You are asked to calculate: "if you randomly select a red shape, what is the probability it is a diamond". Using "R" for red and "D" for diamond, which is the proper set notation for this probability?

Given the data from the contingency table to the left, if you randomly select a shape, what is the probability it is either yellow or a triangle?

•  20%

• 40%

• 60%

• 80%

Answer explanation

The question doesn't restrict the selection to any shape or color, so we can deduce that the possible outcomes is the sample space - so there are 10 possible outcomes.

We are being asked for the probability we select either a yellow shape OR a triangle. Union (symbol: "∪") gives us this "OR".

So, in set notation, we would write: P( Y ∪ T )

We can use the "Addition Rule of Probability" to find the answer:

P(Y∪T) = P(Y)+P(T)-P(Y∩T)

From the chart, P(Y)=5/10, P(T)=3/10, and P(Y∩T)=2/10, so:

P(Y∪T) = 5/10+3/10-2/10 = 6/10

The final probability is 6/10, or 60%.

Don't forget that you can't just add the number of yellow shapes to the number of triangles because you'll be counting the yellow triangles twice!

NOTE: notice that you could get the same answer by adding the number of red triangles, yellow triangles, and yellow diamonds together to get 6, and divide by the possible outcomes, 10.

You are asked to calculate: "the probability of randomly selecting a red shape or a diamond from a number of colored shapes". Using "R" for red and "D" for diamond, which is the proper set notation for this probability?

Given the data from the contingency table to the left, if you randomly select a shape, what is the probability it is a yellow triangle?

•  20%

• 40%

• 60%

• 80%

Answer explanation

The question doesn't restrict the selection to any shape or color, so we can deduce that the possible outcomes is the sample space - so there are 10 possible outcomes.

We are being asked for the probability we select a yellow triangle - in other words, a shape that is yellow AND a triangle. Intersection (symbol: "∩") gives us this "AND".

So, in set notation, we would write: P( Y ∩ T )

We find that there are 2 yellow triangles, so the number of favorable outcomes is 2.

The probability of an event is: the number of favorable outcomes divided by the number of possible outcomes.

So, for this question we have a probability of 2/10, or 20%.