Probability Practice

An ____________ event is when the 1st event DOES NOT affect the 2nd event.

Answer explanation

An independent event is one where the occurrence of the first event does not influence the occurrence of the second event. Therefore, the correct term to fill in the blank is 'independent'.

In a _______________, order DOES NOT matter when counting possibilities.

Answer explanation

In a combination, the order of selection does not matter, meaning that choosing A and B is the same as choosing B and A. This distinguishes combinations from permutations, where order is important.

But in a _____________, order DOES matter when counting possibilities.

Answer explanation

In a permutation, the arrangement of items is important, meaning that different orders count as different possibilities. This contrasts with combinations, where order does not matter.

If the outcome of one event does not affect the outcome of the other event, the events are ________?

• Dependent Events

• Independent Events

• Simple Events

• Complementary Events

Answer explanation

If the outcome of one event does not affect the outcome of another, the events are called Independent Events. This means that knowing the result of one event provides no information about the other.

if the outcome of the first event affects the outcome of the second event, then that is a(n) _______________ .

• Independent Event

• Dependent Event

• Complimentary Event

• Tree Diagram

Answer explanation

A dependent event occurs when the outcome of one event influences the outcome of another. In this case, since the first event affects the second, it is classified as a dependent event.

Which of the following is an example of independent events?

• Flipping a coin and rolling a die

• Choosing two marbles from a bag without replacement

• Drawing two cards from a deck without replacement

• Picking two students from a class without replacement

Answer explanation

Independent events are those where the outcome of one does not affect the other. Flipping a coin and rolling a die are independent because the result of the coin flip does not influence the die roll.

What is the probability of rolling a 3 on a die and then flipping a head on a coin?

• 1/6

• 1/36

• 1/2

• 1/12

Answer explanation

The probability of rolling a 3 on a die is 1/6, and the probability of flipping a head on a coin is 1/2. To find the combined probability, multiply: (1/6) * (1/2) = 1/12. Thus, the correct answer is 1/12.

Which of the following statements is true about dependent events?

• The occurrence of one event does not affect the other

• They have no impact on each other

• The occurrence of one event affects the probability of the other

• They are always mutually exclusive

Answer explanation

Dependent events are those where the occurrence of one event affects the probability of the other. This distinguishes them from independent events, where the events do not influence each other.

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?

• 8/15

• 6/11

• 3/4

• 2/3

Answer explanation

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

What are non mutually exclusive events?

• Events that can happen at the same time

• Events that cannot happen at the same time

• Events that add up to 100%

Answer explanation

Non mutually exclusive events are those that can occur simultaneously. This means that the occurrence of one event does not prevent the occurrence of another, making the correct choice "Events that can happen at the same time."