Free Practice Question

PS · Problem Solving

705-805

Probability

A jar contains slips of paper numbered from 1 to 200, inclusive. If a single slip is drawn at random, what is the approximate probability that the number on it is neither divisible by 2 nor by 5?

Answer Choices

Correct answer marked below

40%

Correct

B

50%

C

60%

D

70%

E

80%

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Explanation

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Official Explanation

Official

To solve the problem, we need to determine the probability that a randomly drawn slip from a jar containing numbers from 1 to 200 is neither divisible by 2 nor by 5. Here's a step-by-step explanation:

Step 1: Determine the Total Number of Slips

The jar contains slips numbered from 1 to 200, inclusive. Therefore, the total number of slips is:

N_{\text{total}} = 200

Step 2: Calculate the Number of Multiples of 2

A number is divisible by 2 if it is even. The number of multiples of 2 between 1 and 200 is:

N_{2} = \left\lfloor \frac{200}{2} \right\rfloor = 100

Step 3: Calculate the Number of Multiples of 5

A number is divisible by 5 if it ends with 0 or 5. The number of multiples of 5 between 1 and 200 is:

N_{5} = \left\lfloor \frac{200}{5} \right\rfloor = 40

Step 4: Calculate the Number of Multiples of Both 2 and 5 (i.e., Multiples of 10)

A number divisible by both 2 and 5 is divisible by 10. The number of multiples of 10 between 1 and 200 is:

N_{10} = \left\lfloor \frac{200}{10} \right\rfloor = 20

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