L8.7 - Related Events

A bag contains 1 crayon of each color: red, orange, yellow, green, blue, pink, black, and purple. 1. A person chooses a crayon at random out of the bag, uses it for a bit, then puts it back in the bag. A second person comes to get a crayon chosen at random out of the bag. What is the probability the second person gets the yellow crayon?

2. A person chooses a crayon at random out of the bag and walks off to use it. A second person comes to get a crayon chosen at random out of the bag. What is the probability the second person gets the yellow crayon?

1. Each of the letters A through J are printed on tiles that are placed in a hat. Andre selects a tile at random and then replaces it. Clare then selects a tile at random. a. What is the probability that Andre selects a tile labeled B?

b. What is the probability that Clare selects a tile labeled B?

c. What is the probability that both Andre and Clare select a tile labeled B?

d. Are the events of Andre selecting a tile and Clare selecting a tile dependent or independent? Explain your reasoning.

2. The Bulldogs have won approximately 67% of their 30 baseball games this season. The Bulldogs won 9 of the 10 games they played when Diego was the starting pitcher. Are the events “the Bulldogs win the game” and “the Bulldogs win the game when Diego is the starting pitcher” dependent or independent events? Explain your reasoning.

A woman is selected at random from the population of the United States. Let event A represent "The woman is a professional basketball player" and event B represent "The woman is taller than 5 feet 4 inches." 1. Are these probabilities equal? If so, explain your reasoning. If not, explain which one is the greatest and why.

• P(B) when you have no other information.
• P(B) when you know A is true.
• P(B) when you know A is false.

2. Are events A and B independent events or dependent events? Explain your reasoning.