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Q.

A box contains 88 discs numbered from 1 to 88. A disc is drawn at random from the box. What is the probability that the number on the disc is not divisible by 8?

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a

712

b

78

c

34

d

29

answer is A.

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Detailed Solution

Given that a box contains 88 discs numbered from 1 to 88.
We need to find the probability that if a disc is drawn at random from the box, it has a number not divisible by 8.
Probability of an event E is defined as:

P (E) = \frac{Number of favorable outcomes}{Total number of possible outcomes}

Since there are 88 discs in the box, therefore, the total number of possible outcomes is 88.
Number of discs that are divisible by 8 are:

8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88

So, there are total 11 numbers that are divisible by 8.
Number of discs that have numbers not divisible by 8 are:
88 – 11 = 77
Therefore, the number of favorable outcomes are 77.
Let

E

be the event that the disc has a number not divisible by 8.
Now, the probability of getting a disc which has number not divisible by 8 is:

P E = 7788 ⇒ P (E) = 78

The probability of getting a disc which has a number not divisible by 8 is

78

.
Therefore, option 1 is correct.

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