Understanding Mutually Exclusive Events

Front

What are mutually exclusive events?

Back

Mutually exclusive events are events that cannot occur at the same time. If one event occurs, the other cannot.

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.4

Front

If P(A) = 0.3 and P(B) = 0.4, what is P(A ∩ B) for mutually exclusive events?

Back

P(A ∩ B) = 0, because mutually exclusive events cannot happen simultaneously.

Tags

CCSS.HSS.CP.B.7

Front

How do you calculate the probability of neither event A nor event B occurring?

Back

Use the formula: P(neither A nor B) = 1 - P(A ∪ B). For events A and B, P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

Tags

CCSS.HSS.CP.B.7

Front

What is the formula for the probability of the union of two events?

Back

P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

Tags

CCSS.HSS.CP.B.7

Front

In a Venn diagram, if the area exclusive to A is 0.3 and the area of overlap is 0.2, what is P(A)?

Back

P(A) = Area exclusive to A + Area of overlap = 0.3 + 0.2 = 0.5.

Tags

CCSS.HSS.CP.A.1

Front

What does it mean if P(A ∩ B) = 0?

Back

It means that events A and B are mutually exclusive; they cannot occur together.

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.4

Front

How do you find the probability of either event A or event B occurring?

Back

Use the formula: P(A or B) = P(A) + P(B) - P(A ∩ B).

Tags

CCSS.HSS.CP.B.7

Front

What is the probability of an event occurring if its complement is known?

Back

If P(A') is the probability of the complement of A, then P(A) = 1 - P(A').

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.4

Front

In a two-way frequency table, how do you calculate the probability of a specific event?

Back

Divide the frequency of the event by the total frequency in the table.

Tags

CCSS.8.SP.A.4

Front

What is the probability of selecting a female or someone who likes dogs from a two-way frequency table?

Back

Use the formula: P(Female or Likes Dogs) = P(Female) + P(Likes Dogs) - P(Female and Likes Dogs).

Tags

CCSS.HSS.CP.B.7