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Out of all the $2$-digit integers between $1$ and $100,$ a $2$-digit number has to be selected at random. What is the probability that the selected number is not divisible by $7$ ?

1. $\left(\dfrac{13}{90}\right)$
2. $\left(\dfrac{12}{90}\right)$
3. $\left(\dfrac{78}{90}\right)$
4. $\left(\dfrac{77}{90}\right)$
edited | 1.2k views
+4

Total 2-digit integers between 1 and 100 =  90 integer,

P = 1 - Q

Where, P = probability that the selected number is not divisible by 7)

Q =  probability that the selected number is  divisible by 7)

TOTAL NUMBER BETWEEN 10 AND 100 WHICH IS DIVISIBLE BY 7 = 13

Q =  (TOTAL NUMBER BETWEEN 10 AND 100 WHICH IS DIVISIBLE BY 7) / Total 2-digit integers between 1 and 100

Q = 13/90                    then,         P = 1 - Q = 1 - 13/90

P = 77/90      Ans.

The number of $2$ digit multiples of 7 $= 13$

not divisible by $7$=$\dfrac{(90-13)}{90}=\dfrac{77}{90} Answer(D)$
edited
+1 vote

There are total 90 two-digit numbers(10 to 99)as(99-10+1=90)because 10 and 99 both included

The number of 2 digit multiples of 7 =13,  these are 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98.

Probability Of An Event
 P(A) = The Number Of Ways Event A Can Occur The total number Of Possible Outcomes

Therefore, the probability that selected number is not divisible by 7 = 1 – (13/90) = 77/90.
So, option (D) is true.

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