Mutually & Non-Mutually Exclusive & Complementary Events

Which formula do you use when two events are mutually exclusive?

Choose all that apply.

• P(A or B) = P(A) + P(B)

• P(A or B) = P(A) + P(B) - P(A and B)

• P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

• P(A ∪ B) = P(A) + P(B)

Answer explanation

For mutually exclusive events, the probability of either event occurring is simply the sum of their individual probabilities. Thus, P(A or B) = P(A) + P(B) and P(A ∪ B) = P(A) + P(B) are correct.

Tags

CCSS.HSS.CP.B.7

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

• 2/8 + 4/8 - 4/8

• 4/8 + 2/8 - 4/8

• 4/8 + 6/8 + 2/8

• 4/8 + 4/8 - 2/8

Answer explanation

To find P(shaded number or number less than five), add the probability of shaded numbers (4/8) to the probability of numbers less than five (4/8), then subtract the overlap (2/8) to avoid double counting. Thus, 4/8 + 4/8 - 2/8 is correct.

Tags

CCSS.7.SP.C.5

CCSS.7.SP.C.8

CCSS.7.SP.C.6

A bag contains 9 green marbles, 5 yellow marbles and 6 red marbles. You choose one marble. What is the probability of selecting a green or red marble?

• 1/4

• 2/4

• 3/4

• 1

Answer explanation

The total number of marbles is 20 (9 green + 5 yellow + 6 red). The number of favorable outcomes for green or red marbles is 15 (9 green + 6 red). Thus, the probability is 15/20, which simplifies to 3/4.

Tags

CCSS.7.SP.C.5

CCSS.7.SP.C.8

There are 5 red roses, 3 yellow roses, and 8 white roses in a tray. What is the probability of picking a white rose or a red rose?

• 13/16

• 12/16

• 11/16

• 14/16

Answer explanation

To find the probability of picking a white or red rose, add the number of red (5) and white (8) roses, giving 13. The total number of roses is 16. Thus, the probability is 13/16, which is the correct answer.

Tags

CCSS.7.SP.C.5

CCSS.7.SP.C.8

CCSS.7.SP.C.7

Find the probability of drawing a five or a heart from a standard deck of 52 cards.

• 13/52

• 17/52

• 4/13

• 16/52

• 4/52

Answer explanation

To find the probability of drawing a five or a heart, note there are 4 fives and 13 hearts. However, the five of hearts is counted twice, so total = 4 + 13 - 1 = 16. Thus, P = 16/52 = 4/13.

Tags

CCSS.7.SP.C.5

CCSS.7.SP.C.8

CCSS.7.SP.C.7

Two events are mutually exclusive if:

• they happen at the same time

• they cannot happen at the same time

• they sometimes happen at the same time 

• they always happen

Answer explanation

Two events are mutually exclusive if they cannot happen at the same time. This means that if one event occurs, the other cannot occur simultaneously, making the correct choice "they cannot happen at the same time."

Which of the following pairs of events is mutually exclusive?

• Cards: Aces and Spades

• Two dice: Odd and even

• Sit down and stand up

• Sit down and scratch your nose

Answer explanation

The events 'sit down' and 'stand up' are mutually exclusive because you cannot perform both actions simultaneously. If you are sitting, you cannot be standing, and vice versa.

Which of the following shows how to determine P(diamond or J, Q, K 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

Answer explanation

To find P(diamond or J, Q, K), add the probability of drawing a diamond (13/52) and the probability of drawing a J, Q, or K (12/52), then subtract the overlap (3/52) for J, Q, K that are also diamonds.

Tags

CCSS.7.SP.C.5

CCSS.7.SP.C.8

CCSS.7.SP.C.7

A​ (a)   is an event that​ cannot happen at the same time. An example would be flipping a ​ (b)   and getting​ heads and ​ (c)   .

• mutually exclusive event
• tails
• non-mutually exclusive event

• inclusive event

• actions

• probability

• coin
• card

• heads

Answer explanation

A mutually exclusive event cannot occur simultaneously. Flipping a coin results in either heads or tails, but not both at the same time, illustrating this concept.

Match the following:

• = 0

• and

• Probability of complement of event A

• P(A) + P(A')

• = 1

• or

• P(A')

• Mutually exclusive events P(A) + P(B)