A box contains 80 discs numbered from 1 to 80. If one disc is drawn at random from the box, find the probability that it bears a number divisible by 2 and 3.

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\frac{1}{80}

\frac{13}{80}

\frac{9}{80}

\frac{11}{80}

answer is B.

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Detailed Solution

Given, a box contains 80 discs numbered from 1 to 80. If one disc is drawn at random from the box.
The probability of an event to be occurred is the division of the number of favourable outcomes by the total number of outcomes that is,

Probability of an cvent = Number of favourable outcomes Total number of outcomes

Finding the number of favourable outcomes:
Total number of discs from 1 to 80 is 80.
The numbers from the discs which are divisible by 2 and 3 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72 and 78.
So, the number of favourable outcomes is 13.
Find the required probability by dividing the favourable outcomes by the total number of numbers that is, 13 and 80 respectively.