There are 49 cards in a box numbered from 1 to 49. Every card is numbered with only 1 number. The probability of picking up a card, the number printed on which is a multiple of 5 but not that of 10 or 15 is _____.
Question
There are 49 cards in a box numbered from 1 to 49. Every card is numbered with only 1 number. The probability of picking up a card, the number printed on which is a multiple of 5 but not that of 10 or 15 is _____.
Solution
Step 1: Identify the total number of outcomes
In this case, the total number of outcomes is 49 because there are 49 cards.
Step 2: Identify the favorable outcomes
We need to find the cards that are multiples of 5 but not multiples of 10 or 15. The multiples of 5 between 1 and 49 are 5, 10, 15, 20, 25, 30, 35, 40, 45. Out of these, 10, 15, 20, 30, 40, 45 are multiples of 10 or 15. So, the favorable outcomes are 5, 25, 35.
Step 3: Calculate the probability
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of outcomes. So, the probability of picking a card that is a multiple of 5 but not a multiple of 10 or 15 is 3/49.
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