Question

# A number is selected at random from the first $$1,000$$ natural numbers. What is the probability that the number so selected would be a multiple of $$7$$ or $$11$$?

A
0.25
B
0.32
C
0.22
D
0.33

Solution

## The correct option is C $$0.22$$Given: First $$1000$$ natural numbersTo find: the probability that the number so selected would be a multiple of $$7$$ or $$11$$Sol: According to the question, $$n(S)=1000$$Number of multiples of $$7$$ in first $$1000$$ natural numbers, $$P(A)=\left\lfloor\dfrac {1000}7\right\rfloor\approx 142$$Number of multiples of $$11$$ in first $$1000$$ natural numbers, $$P(B)=\left\lfloor\dfrac {1000}{11}\right\rfloor\approx 90$$And, numbers divisible by $$7$$ and $$11$$ are $$P(A\cap B)=\left\lfloor\dfrac {1000}{11\times 7}\right\rfloor\approx 12$$Hence the probability that the number so selected would be a multiple of $$7$$ or $$11$$ $$=P(A)+P(B)-P(A\cap B)=\dfrac {142}{1000}+\dfrac {90}{1000}-\dfrac {12}{1000}=\dfrac {142+90-12}{1000}=0.22$$Maths

Suggest Corrections

0

Similar questions
View More