Question

probability HOTS...

Answer 5 and 6 with sample space

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Answer 1

$\bold{\boxed{Answer}}$

5)

multiple of 3 and 4

means numbers that are multiple of both the numbers (i.e. 3 and 4) or we can say that numbers that are multiple of LCM of given number (here LCM of 3 and 4 is 12)

so

we have to find numbers that are multiple of 12.

those numbers are

12, 24, 36 .......upto 120

let total numbers of such numbers be n

120 = 12 + (n-1)(12). [by the formula of nth term]

(n-1)(12) = 108

n-1 = 9

n = 10

there are 10 such numbers

probability of multiple of

3 and 4 = 10/120

$\bold{\boxed{=\:1/12}}$

6)

multiple of 3 or 4

means numbers that are either multiple of 3 or 4 and both

multiple of 3 are 3,6,9.....upto 120 ....(1)

multiple of 4 are 4,8,12....upto 120 ...(2)

firstly find number of multiples of both then add them. After adding you will get twice the multiple of 12 in your sum because 12 and it's multiple comes in both the multiple of given numbers.

then we have to subtract number of multiples of 12 one time from the added multiples.

so that we will get correct number of multiples of 3 or 4

solution

for ..(1). for ...(2)

120 = 3 + (n-1)(3). 120 = 4 + (n-1)+(4)

117 = (n-1)+3). 116 = (n-1)(4)

(n-1) = 39. (n-1) = 29

n = 40. n = 30

total multiples of 3 or 4 = 40 + 30 - multiple of 12(i.e. multiple of 3 and 4)

total multiples of 3 or 4 = 70 - 10 = 60

probability of multiples of

3 or 4 = 60/120

$\bold{\boxed{=\:1/2}}$

$\bold{\boxed{hope\:this\:will\:help\:you}}$

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