In Exercises 21-28, find the probability and answer the questi...

Question

In Exercises 21-28, find the probability and answer the questions.

Guessing Birthdays On their first date, Kelly asks Mike to guess the date of her birth, not including the year.

b. Would it be unlikely for him to guess correctly on his first try?

Accepted Answer

Welcome back, everyone. During a school tour, a student challenges her friends to guess the three digit code of her locker on his first attempt. Each digit in the code ranges from 0 to 9, and digits can be repeated. Would it be unlikely for her friend to guess the correct combination on his first try? For this problem, we want to identify the total number of ways to form a 3 digit code. Now we have 3 slots, and from 0 to 9, we have a total of 10 elements, right? 10 different numbers. We can identify that by taking 9 minus 0 + 1, right? And this gives us 10. There are 10 possible digits, so we have 10 elements and we have 3 slots. So what we want to do is simply recall that the formula that allows us to identify the total number of ways to fill K slots with N elements is N to the power of K when repetition is allowed. So our N is equal to 10. We have 10 different numbers and our key, the number of slots is 3. So the total number of ways. To form a 3 digit code when the repetition is allowed is simply 10 to the power of 3, which can also be derived from the multiplication rule, right? 10, multiplied by 10, multiplied by 10. And that's 1000. We have to understand that only one code is correct, right? So the probability of being correct. On his first try is equal to 1 because we only have one favorable outcome divided by the total number of outcomes, so 1 divided by 1000, which is 0.001. If we express this in its percentage form, we basically multiply it by 100, which gives us 0.1%. So this probability is extremely low because it's really close to 0, right, meaning it is unlikely for her friend to guess the correct combination on his first try. So the answer to this problem is yes. That'd be our final answer and thank you for watching.

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In Exercises 21-28, find the probability and answer the questions.

Guessing Birthdays On their first date, Kelly asks Mike to guess the date of her birth, not including the year.

b. Would it be unlikely for him to guess correctly on his first try?

Key Concepts

Probability

Sample Space

Unlikely Events

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In Exercises 21-28, find the probability and answer the questions.Guessing Birthdays On their first date, Kelly asks Mike to guess the date of her birth, not including the year.b. Would it be unlikely for him to guess correctly on his first try?