Determining Independence of Events A and B Using Complements

This lesson teaches how to determine if events A and B are independent using complements. It reviews conditional probability and independence, emphasizing strategic use of complements to simplify calculations. The lesson includes examples, such as calculating the probability of rolling dice and analyzing the impact of sunscreen on sunburn probability. It concludes that different SPSF levels do not significantly affect sunburn probability, highlighting the importance of understanding complements in probability.

What is the purpose of using complements in probability calculations?

• To avoid using conditional probabilities

• To simplify the calculation process

• To increase the probability of an event

• To ensure events are dependent

In the dice example, what is the complement of rolling at least one five in three tosses?

• Rolling at least two fives

• Rolling no fives

• Rolling exactly one five

• Rolling at least one six

How can you determine if two events are independent?

• By finding the product of their probabilities

• By ensuring their probabilities add up to one

• By calculating the sum of their probabilities

• By checking if their conditional probabilities are equal

What conclusion is drawn about the effectiveness of different SPSF levels in preventing sunburn?

• Higher SPSF levels significantly reduce sunburn probability

• SPSF levels do not affect sunburn probability at all

• Lower SPSF levels are more effective

• There is no significant difference between SPSF 15 and SPSF 45

What percentage of participants who wore SPSF 15 got a sunburn?

• 10%

• 20%

• 30%

• 40%