Free Practice Question

PS · Problem Solving

705-805

Probability

A jar contains slips of paper numbered from 1 to 100, inclusive. If a slip is drawn randomly, what is the approximate probability that the number on it is not divisible by 2 or 3?

Answer Choices

Correct answer marked below

\frac{1}{3}

Correct

B

\frac{1}{2}

C

\frac{2}{3}

D

\frac{1}{4}

E

\frac{1}{6}

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Explanation

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Official Explanation

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To solve the problem of finding the probability that a randomly drawn slip from a jar containing numbers from 1 to 100 is not divisible by 2 or 3, we can follow these steps:

Total Numbers in the Jar:

- The jar contains numbers from 1 to 100, inclusive. So, there are

100

possible numbers.

Numbers Divisible by 2:

- To find how many numbers are divisible by 2, we calculate:

\text{Number of multiples of 2} = \left\lfloor \frac{100}{2} \right\rfloor = 50

- So, there are

50

numbers divisible by 2.

Numbers Divisible by 3:

- To find how many numbers are divisible by 3, we calculate:

\text{Number of multiples of 3} = \left\lfloor \frac{100}{3} \right\rfloor = 33

- So, there are

33

numbers divisible by 3.

Numbers Divisible by Both 2 and 3 (i.e., Divisible by 6):

- To find how many numbers are divisible by both 2 and 3, we calculate:

\text{Number of multiples of 6} = \left\lfloor \frac{100}{6} \right\rfloor = 16

- So, there are

16

numbers divisible by both 2 and 3.

Total Numbers Divisible by 2 or 3:

- Using the principle of inclusion-exclusion, the total number of numbers divisible by 2 or 3 is:…

A jar contains slips of paper numbered from 1 to 100, inclusive. If a slip is drawn randomly, what is the approximate probability that the number on it is not divisible by 2 or 3?

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