a roulette wheel has 40 slots evenly divided between red (even) and green (odd) slots totaling 38 and a "0" and a "00". what is the probability of the ball landing in an:
A)even number < 10
B) other than an even or odd number
C) odd number > 15
D) even number greater than or equal to 12
E) odd number less than or equal to 13
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Each of the following numbers will be divided by the total possibilities (40).
A) 2, 4, 6, or 8 = 4
B) 0 or 00 = 2
To find the probability of an event occurring in a roulette wheel with 40 slots, we need to determine the total number of favorable outcomes (slots that satisfy the event) and divide it by the total number of possible outcomes (total number of slots).
A) The favorable outcomes for an even number less than 10 are the even numbers 2, 4, 6, and 8. Therefore, there are 4 favorable outcomes. The total number of possible outcomes is 40 (since there are 40 slots in total). Thus, the probability is 4/40 = 1/10.
B) The favorable outcomes for a number other than even or odd are the numbers 0 and 00. Therefore, there are 2 favorable outcomes. The total number of possible outcomes is still 40. So, the probability is 2/40 = 1/20.
C) The favorable outcomes for an odd number greater than 15 are the odd numbers 17, 19, 21, ..., 37. Notice that we have a total of 21 odd numbers greater than 15. So, there are 21 favorable outcomes, and the probability becomes 21/40.
D) The favorable outcomes for an even number greater than or equal to 12 are the even numbers 12, 14, ..., 38. Notice that we have a total of 20 even numbers greater than or equal to 12. Therefore, there are 20 favorable outcomes, and the probability is 20/40 = 1/2.
E) The favorable outcomes for an odd number less than or equal to 13 are the odd numbers 1, 3, 5, 7, 9, 11, and 13. Thus, there are 7 favorable outcomes, and the probability is 7/40.
To summarize:
A) Probability of an even number < 10: 1/10
B) Probability of a number other than even or odd: 1/20
C) Probability of an odd number > 15: 21/40
D) Probability of an even number ≥ 12: 1/2
E) Probability of an odd number ≤ 13: 7/40