A lottery hopper uses balls numbered 1–50. After each ball is chosen, it is not replaced. Which of the following is the probability that the number 13 is not selected on either of the first two draws?

Rationale

The probability that the number 13 is not selected on either of the first two draws is 2,352/2,450.

To find this probability, we can calculate the likelihood of not selecting the number 13 in two consecutive draws from a pool of 50 balls. After the first draw, there are 49 balls remaining, and the probability of not drawing the number 13 on both draws is obtained by multiplying the probabilities of each individual event.

A (48/50) YOUR ANSWER

This choice represents the probability of not selecting the number 13 on the first draw only. However, it does not account for the second draw where the number of remaining balls changes, making this choice incomplete for the scenario involving two draws.

B (02-Jan) YOUR ANSWER

This option appears to be nonsensical as it mixes numerical and alphabetical formats without conveying a valid probability. Therefore, it does not represent any meaningful calculation related to the problem.

C (2,498/2,500) YOUR ANSWER

Although this fraction simplifies to 0.9992, it does not represent the correct scenario. This choice incorrectly assumes an independent selection process without accounting for the reduced number of total balls after the first draw, leading to an inaccurate probability calculation.

D (2,352/2,450) CORRECT

This choice correctly calculates the probability of not selecting the number 13 on either of the first two draws. The first draw offers a 48 out of 50 chance of not drawing 13, and the second draw offers a 47 out of 49 chance, leading to a combined probability of (48/50) * (47/49) = 2,352/2,450.

Conclusion

In summary, determining the probability that the number 13 is not selected on either of the first two draws requires careful consideration of the changing pool of balls. The correct answer, 2,352/2,450, accounts for the diminishing number of options after each draw, accurately reflecting the sequential nature of the selections. Other options either miscalculate or fail to address the dependency of the draws.

A lottery hopper uses balls numbered 1–50. After each ball is chosen, it is not replaced. Which of the following is the probability that the number 13 is not selected on either of the first two draws?

The probability that the number 13 is not selected on either of the first two draws is 2,352/2,450.

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