A number is chosen at random from 1 to 120. Theprobability of the number chosen being a multipleof 3 and 15 both is _
Question
A number is chosen at random from 1 to 120. Theprobability of the number chosen being a multipleof 3 and 15 both is _
Solution
To find the probability of a number being a multiple of both 3 and 15, we first need to find the numbers that are multiples of both within the given range (1 to 120).
The least common multiple (LCM) of 3 and 15 is 15. So, we need to find the multiples of 15 from 1 to 120.
The multiples of 15 within this range are: 15, 30, 45, 60, 75, 90, 105, and 120. That's a total of 8 numbers.
The total number of possible outcomes (numbers from 1 to 120) is 120.
The probability of an event is given by the formula: P(E) = Number of favorable outcomes / Total number of outcomes
So, the probability of the number chosen being a multiple of both 3 and 15 is 8/120 = 1/15.
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