Cards marked with numbers $5, 6, 7, …, 74$ are placed in a bag and mixed thoroughly. One card is drawn at random from the bag. Find the probability that the number on the card is a perfect cube.

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270

370

170

570

answer is B.

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Detailed Solution

Given, cards marked with numbers

5, 6, 7, …, 74

are placed in a bag and mixed thoroughly. One card is drawn at random from the bag.
The probability of an event occurring is calculated by dividing 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

Find the number of positive outcomes.
Total number of numbers from 5, 6, 7..., 74 is 70.
The numbers that are perfect cubes from 5, 6, 7..., 74 are 8, 27 and 64 that is,

23, 33

, and

43

.
This means that the number of perfect cubes from 5, 6, 7..., 74 is 3, indicating that the number of favourable outcomes is three.
Find the required probability by dividing the positive outcomes by the total number of numbers, 3 and 70 are obtained.