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ack wakes up late on average 3 days in every 5. If Jack wakes up late, the probability he's late for school = 9/10 If Jack does not wake up late, the probability he's late for school = 3/10 One what percent of days does Jack get to school on time? 80% 34% 50% 66%

Question

ack wakes up late on average 3 days in every 5.

If Jack wakes up late, the probability he's late for school = 9/10

If Jack does not wake up late, the probability he's late for school = 3/10

One what percent of days does Jack get to school on time?

80% 34% 50% 66%

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Solution

To solve this problem, we need to calculate the probability of Jack getting to school on time on the days he wakes up late and on the days he doesn't wake up late.

  1. First, calculate the probability of Jack waking up late and getting to school on time. This is the product of the probability of him waking up late (3/5) and the probability of him getting to school on time given that he woke up late (1 - 9/10 = 1/10). So, (3/5) * (1/10) = 3/50.

  2. Next, calculate the probability of Jack not waking up late and getting to school on time. This is the product of the probability of him not waking up late (2/5) and the probability of him getting to school on time given that he didn't wake up late (1 - 3/10 = 7/10). So, (2/5) * (7/10) = 14/50.

  3. Add these two probabilities together to get the total probability of Jack getting to school on time: (3/50) + (14/50) = 17/50.

  4. To convert this probability to a percentage, divide 17 by 50 and multiply by 100: (17/50) * 100 = 34%.

So, Jack gets to school on time on 34% of days. The correct answer is 34%.

This problem has been solved

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