Outcomes in roulette. One game that is popular in many American casinos is roule

Question

Outcomes in roulette. One game that is popular in many American casinos is roulette. Roulette is played by spinning a ball on a circular wheel that has been divided into 38 arcs of equal length: these bear the numbers 00, 0, 1, 2, ..., 35, 36. The number on the are at which the ball comes to rest is the outcome of one play of the game. The numbers are also colored in the following manner: Players may place bets on the table in a variety of ways, including bets on odd, even, red, black, low (1-18), and high (19-36) outcomes. Consider the following events (00 and 0 are considered neither odd nor even): (Outcome is an odd number) (Outcome is a black number) (Outcome is a high number) Calculate the probabilities of the following events:

Explanation / Answer

There are total 38 outcomes

For event A or B, there are 36 outcomes

P( A or B) =36/38 =0.9474

For event A and C, there are 9 outcomes

P( A and C) =9/38 =0.2368

For event B or C, there are 27 outcomes

P( B or C) =27/38 =0.7105

For event Bc, there are 20 outcomes

P( Bc) =20/38 =0.5263

For event (A and B and C), there are 0 outcome

P( A and B and C) =0/38 = 0

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