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Probability

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Question : 109 of 127

Marks: +1, -0

Out of numbers 1 to 120, one is selected at random, what is the probability that it is divisible by 8 or 10 ?

$0.9$
$0.2$
$0.6$
$0.7$

Solution:

Concept:

Use principle of inclusion-exclusion to count numbers divisible by 8 or 10.

Explanation:

Total numbers from 1 to 120:

120

.

Multiples of 8:

\lfloor \frac{120}{8} \rfloor = 15

.

Multiples of 10:

\lfloor \frac{120}{10} \rfloor = 12

.

LCM of 8 and 10 is

40

, so multiples of both:

\lfloor \frac{120}{40} \rfloor = 3

.

Favorable numbers:

15 + 12 - 3 = 24

.

Probability:

\frac{24}{120} = 0.2

.

Answer:

0.2

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