Probability of Overlapping Events

If you are picking a card randomly from a deck of cards, the events of picking a jack or picking a heart are mutually exclusive because there is no way you can pick a jack card that is also a heart card.

• True

• False

If you are picking a card randomly from a deck of cards, the events of picking an ace or picking a ‘3’ are mutually exclusive because there is no way you can a pick a card that is both a 3 and an ace.

• True

• False

If you are picking a card randomly from a deck of cards, the events of picking a spade or picking a diamond are mutually exclusive.

• True

• False

When rolling a single die, the events of rolling an even number or rolling a ‘5’ are mutually exclusive.

• True

• False

When rolling a single die once, the events of rolling an odd number or rolling a prime are mutually exclusive.

• True

• False

To find the probability of mutually exclusive events, denoted by P(A or B); find the probability of each event and add these, P(A) + P(B).

• True

• False

To find the probability of overlapping events, you can add the probability of each event and subtract the overlap, also known as the "intersection, ∩".

• False

• True

When determining the probability of mutually exclusive and overlapping events you should sketch a Venn diagram to help you understand the problem.

• True

• False

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

• 26/52 + 12/52 - 6/52

• 3/52 + 13/52 -12/52

• 26/52 + 12/52 - 13/52

• 1/13 + 3/52 - 1/2

In finding P(black or face card) on a standard deck of cards, are we dealing with mutually exclusive or overlapping events? Explain why.

• Exclusive events because it is not possible to choose a card that is both a black card and a face card.

• Exclusive events because there are 6 cards that are either black or face cards, but not both.

• Overlapping events because there are 26 cards that are both black and face cards.

• Overlapping events because there are 6 cards that are both black and face cards.