Probability Trees and Marbles

The video tutorial explains probability trees, focusing on calculating probabilities with and without replacement. It covers scenarios involving different events and advanced probability exercises. The tutorial also demonstrates how to multiply probabilities across branches and discusses the importance of probabilities adding up to a whole. Examples include drawing marbles from a bag and playing games like tennis and squash.

What is the primary purpose of a probability tree?

• To determine the color of a marble

• To measure the height of a tree

• To calculate the speed of an object

• To visualize different outcomes of an event

In a probability tree, what does replacing a marble mean?

• Putting the marble back into the bag after drawing

• Changing the color of the marble

• Removing a marble permanently

• Adding a new marble to the bag

How do you calculate the probability of two independent events occurring in sequence?

• By subtracting their probabilities

• By dividing their probabilities

• By adding their probabilities

• By multiplying their probabilities

What changes in the probability tree when marbles are not replaced?

• The probabilities for the second event change

• The total number of marbles remains the same

• The color of the marbles changes

• The tree becomes a circle

When calculating probabilities without replacement, what happens to the total number of marbles?

• It stays the same

• It doubles

• It decreases

• It increases

What is the probability of winning at tennis if the probability of winning is 0.75?

• 0.50

• 1.00

• 0.25

• 0.75

How do you calculate the probability of winning one game if there are two games with different probabilities?

• By adding the probabilities of winning both games

• By subtracting the probability of losing both games

• By adding the probabilities of winning one and losing the other

• By multiplying the probabilities of winning both games

In a probability tree with three branches, what must the sum of probabilities for each branch add up to?

• 0.5

• 3

• 1

• 2

If you draw a red marble first and do not replace it, what happens to the probability of drawing another red marble?

• It becomes zero

• It stays the same

• It decreases

• It increases

What is the probability of drawing one red and one yellow marble in sequence without replacement?

• 9 out of 90

• 21 out of 90

• 42 out of 90

• 63 out of 90