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Probability

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Question : 73 of 127

Marks: +1, -0

A number is selected at random from the first 1000 natural numbers. What is the probability that the number so selected would be

a

multiple of 7 or 11 ?

$0.25$
$0.32$
$0.22$
$0.33$

Solution:

Concept:

Use inclusion-exclusion to find numbers divisible by 7 or 11.

Explanation:

Total numbers from 1 to 1000:

1000

.

Multiples of 7:

\left\lfloor \frac{1000}{7} \right\rfloor = 142

.

Multiples of 11:

\left\lfloor \frac{1000}{11} \right\rfloor = 90

.

Multiples of both (LCM = 77):

\left\lfloor \frac{1000}{77} \right\rfloor = 12

.

Favorable count =

142 + 90 - 12 = 220

.

Probability =

\frac{220}{1000} = 0.22

.

Answer:

0.22

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