Probability and Tree Diagrams

The video tutorial by Mrs. Zapia covers lesson seven on calculating probabilities of compound events. It introduces tree diagrams as a method to organize outcomes in multi-stage experiments, using examples like three nights of games and birth outcomes. The lesson explains how to calculate probabilities for different scenarios and emphasizes the use of tree diagrams for visual representation. The tutorial concludes with additional examples to reinforce the concepts.

What is the primary purpose of using a tree diagram in probability experiments?

• To display possible outcomes of multi-stage experiments

• To determine the color of a die

• To predict the weather

• To calculate the speed of an event

How does the tree diagram change when mapping outcomes for three consecutive nights?

• It only considers card games

• It eliminates the need for a die

• It requires adding a third stage to each branch

• It remains the same as for two nights

Which of the following outcomes represents exactly two board games played over three nights?

• CBC

• BCC

• BBB

• CBB

Why are the eight outcomes of the three nights not equally likely?

• The die used is biased

• All outcomes have the same probability

• The probability of playing board games is higher than cards

• The probability of playing cards is higher than board games

What is the probability of playing at least one night of card games over three nights?

• 0.421875

• 0.875

• 0.578125

• 0.125

In the family birth scenario, what is the probability of having three girls?

• 0.875

• 0.125

• 0.375

• 0.625

How many possible outcomes are there for a family with three children, considering no twins or triplets?

• 4

• 10

• 6

• 8

What is the probability of having at least one girl in a family of three children?

• 0.875

• 0.625

• 0.375

• 0.125

What is the probability of losing a game five consecutive times if the chance of winning is 35%?

• 0.116

• 0.884

• 0.35

• 0.65

What strategy can be used to find the probability of winning at least once in five games?

• Divide the probability of winning by the number of games

• Add the probability of winning and losing

• Subtract the probability of losing five times from one

• Multiply the probability of winning five times