2) The general formula for P(A U B U C) is P(A) + P(B) + P(C) - P(A B) - P(A C) - P(B C) + P(A B C)

Name: 2) The general formula for P(A U B U C) is P(A) + P(B) + P(C) - P(A B) - P(A C) - P(B C) + P(A B C). Using this formula
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Statistics Jan 23, 2021

2) The general formula for P(A U B U C) is P(A) + P(B) + P(C) - P(A $\cap$ B) - P(A $\cap$ C) - P(B $\cap$ C) + P(A $\cap$ B $\cap$ C). Using this formula prove the following:

If A, B, and C are independent events then P(A U B U C) = P(A)+P(A^C)P(B) + P(A^C)P(B^C)P(C)

3) Using the formula for number two, suppose you have the following scenario. You play three games of roulettte (the wheel has 38 slots, numbered 00, 0, and 1 through 36. In the first game, you bet that the winning number will be a positive multiple of three. In the second game you bet that the winning number iwll be a prime number. In the third game, you bet on green (00 and 0 are the green numbers). Find (A U B U C). What does this probability represent?

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