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Find the probability of each event. You've purchased a lottery ticket and your numbers are: 2-4-3. A lottery official randomly selects three balls from a set of seven balls that are numbered from #1 to #7. To win, your numbers must match the selected numbers in order. What is the probability of winning the lottery?

A) 1/35
B) 1/210
C) 1/5040
D) 1/720

1 Answer

4 votes

Final answer:

To calculate the probability of winning the lottery when the winning numbers must match the selected numbers in order from a set of 7, we multiply the individual probabilities of each selection (1/7 for the first number, 1/6 for the second, and 1/5 for the third) for an overall probability of 1/210. The correct choice is B) 1/210.

Step-by-step explanation:

To find the probability of winning the lottery when your numbers are 2-4-3, and the numbers must match in order, we consider that the first number is drawn from a set of 7 numbers, then the second from 6 remaining numbers, and the third from the remaining 5 numbers (since each number is not replaced once it is drawn). The probability of getting the first number right is 1 out of 7 (1/7). The probability of getting the second number correct, assuming the first number was already correctly picked, is 1 out of 6 (1/6), and similarly, the third number is 1 out of 5 (1/5).

To calculate the overall probability, we multiply these individual probabilities:

  1. Probability of first number: 1/7
  2. Probability of second number: 1/6
  3. Probability of third number: 1/5

Therefore, the probability of winning the lottery is: (1/7) * (1/6) * (1/5) = 1/210.

The correct answer is B) 1/210.

User Mike Hanafey
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