Probability and Sample Space Concepts

This video tutorial covers calculating probabilities of compound events using tree diagrams. It includes examples such as house decoration, school scheduling, and game night scenarios to illustrate how tree diagrams can map out possible outcomes. The video also provides exercises and solutions to reinforce learning and discusses advanced probability calculations.

What is the primary tool used to map out sample spaces in compound events?

• Pie Charts

• Bar Graphs

• Tree Diagrams

• Venn Diagrams

In the house decorating example, if the kitchen is painted red, what are the possible colors for the office?

• Red, Blue

• White, Blue

• Only Blue

• Red, White, Blue

How many possible outcomes are there for Ralph's school schedule if he can choose between music, science, and math for two periods?

• 12

• 9

• 6

• 3

What shape is the die used in the family game night scenario?

• Tetrahedron

• Dodecahedron

• Octahedron

• Cube

When extending a tree diagram to three stages, what must be done to accommodate the additional stage?

• Use a different diagram

• Remove some outcomes

• Attach possibilities to each branch of the previous stage

• Add more branches to the first stage

What does the sequence 'CBC' represent in the context of the family game night?

• Card game, Board game, Card game

• Board game, Board game, Card game

• Board game, Card game, Board game

• Card game, Card game, Board game

What is the probability of the sequence 'CBC' occurring?

• 0.046785

• 0.578125

• 0.884

• 0.116

If the probability of winning a game is 0.35, what is the probability of losing it?

• 0.75

• 0.65

• 0.50

• 0.35

How do you calculate the probability of losing a game five consecutive times?

• Multiply the probability of losing once by itself five times

• Add the probability of losing once five times

• Divide the probability of losing once by 5

• Subtract the probability of winning from 1

What is the probability of winning at least once in five games if the probability of losing each game is 0.65?

• 0.421

• 0.884

• 0.578

• 0.116