Kentucky Pick 4 In the Kentucky Pick 4 lottery game, you can pay \$1 for a “straight” bet in which you select four digits with repetition allowed. If you buy only one ticket and win, your prize is \$2500.

c. If you play this game once every day, find the probability of no wins in 365 days.

검증된 단계별 안내

Step 1: Understand the problem. In the Kentucky Pick 4 lottery game, you select four digits with repetition allowed. The total number of possible outcomes is 10^4 (since there are 10 digits, 0 through 9, and repetition is allowed). The probability of winning on a single ticket is 1 divided by the total number of outcomes.

Step 2: Calculate the probability of losing on a single ticket. The probability of losing is the complement of the probability of winning, which is given by P(losing) = 1 - P(winning).

Step 3: Recognize that the problem involves repeated independent trials. If you play the game once every day for 365 days, the probability of no wins in 365 days is the probability of losing every single day. Since the trials are independent, the probability of losing every day is the product of the probability of losing on each day.

Step 4: Use the formula for the probability of no wins in 365 days: P(no wins) = P(losing)^365. Substitute the value of P(losing) from Step 2 into this formula.

Step 5: Simplify the expression for P(no wins) to get the final probability. You can leave the result in terms of powers or logarithms for further calculation if needed.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Probability of Winning

In the Kentucky Pick 4 lottery, the probability of winning a straight bet is calculated by determining the total number of possible combinations of four digits (0000 to 9999), which is 10,000. Therefore, the probability of winning with one ticket is 1 in 10,000, or 0.0001.

Complementary Probability

Complementary probability refers to the likelihood of an event not occurring. In this case, the probability of not winning with one ticket is 1 minus the probability of winning. Thus, the probability of no wins in a single day is 1 - 0.0001 = 0.9999.

Independent Events

In probability theory, independent events are those whose outcomes do not affect each other. Playing the lottery each day is an independent event, meaning the outcome of one day does not influence the next. To find the probability of no wins over 365 days, we raise the daily no-win probability to the power of 365: (0.9999)^365.

Kentucky Pick 4 In the Kentucky Pick 4 lottery game, you can pay \$1 for a “straight” bet in which you select four digits with repetition allowed. If you buy only one ticket and win, your prize is \$2500.c. If you play this game once every day, find the probability of no wins in 365 days.