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a number is taken at random from the number 1 to 150 find the probability that the number is divisible by 4 or 9 |
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Answer» Let there are n numbers divisible by 4 tn = 148 tn = a+ (n-1)d 148=4+(n-1)4 n= 37 So there are 37 no. from 1 to 150 which are divisible by 4 similarly we can find number of numbers divisible by 9 tn = 144 144 =9 + ( n-1) 9 n=16 So there are 16 numbers divisible by 9 between 1 and 150. So total numbers divisible by 9 or 4 are 37 + 16 = 53. but some these are counted two times as there could be numbers which are divisible by both 9 and 4 such as 36. So these numbers divisible by both 9 and 4 are divisible by 36. Let find the number of numbers divisible by 36 between 1 and 150 tn=144 144= 36 + (n-1) 36 n= 4 n(AUB) = n(A) + n(B)- n(AηB) = 37+16-4 = 49 Probability of selecting a number divisible by 9 or 4 between 1 and 150 is probability of selecting 49numbers from 150numbers =49/150 correct answer is 49/150
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