(Use Excel when providing solutions. Utilize Excel functions and formulas) 4.10
ID: 3072603 • Letter: #
Question
(Use Excel when providing solutions. Utilize Excel functions and formulas)
4.10 Roulette The game of roulette uses a wheel containing 38 pockets. Thirty-six pockets are num- bered 1, 2,... , 36, and the remaining two are marked 0 and 00. The wheel is spun, and a pocket is identified as the "winner." Assume that the observance of any one pocket is just as likely as any other. a. Identify the simple events in a single spin of the roulette wheel b. Assign probabilities to the simple events. c. Let A be the event that you observe either a 0 or a 00. List the simple events in the event A and find P(A). d. Suppose you placed bets on the numbers 1 through 18. What is the probability that one of your num- bers is the winner?Explanation / Answer
a)
When a wheel of roulette is spun, there are 38 distinct possible outcomes.
Sample Sapce, S = {0, 00, 1, 2..... , 36}
b)
Probability of getting any numbers as an outcome is 1/38
c)
A = {0, 00}
P(A) = 1/38 + 1/38 = 2/38 = 1/19
d)
A number is winner from 1 through 18, this is possbile in 18C1 ways.
Required probability, = 18C1/38C1 = 18/38 = 9/19
Excel function to calculate combination 18C1 = COMBIN(18,1)
and 38C1 = COMBIN(38,1)
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