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A number is chosen at random from 1 to 10. Find the probability of not selecting

a multiple of 2 or a multiple of 3.

User Dojuba
by
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1 Answer

1 vote

Answer:

0.3

Explanation:

Number of ways of selecting r elements from a set of n different elements is given by

C(n,r)=(n r)=n!/(r!(n−r)!)

No of ways of selecting one number out of ten numbers from one to 10 is 10

It can also be calculated using

C(n,r)=(n r)=n!/(r!(n−r)!)

where n = 10 and r = 1

C(10,1)=(10 1)=10!(1!(10−1)!) = 10*9!/ 1!*9! = 10

multiples of 2 in range 1 to 10 are 2, 4, 6, 8 , 10

multiples of 3 in range 1 to 10 are 3, 6, 9

Therefore number which are multiple of 2 and 3 are

2, 3,4,6,8,9,10 ( 7 numbers)

therefore no of ways of selecting multiple of 2 and 3 is 7 ways

number which are not multiple of 2 and 3 in range 1 to 10

1,5,7 (3 numbers)

no of ways of not selecting multiple of 2 and 3 is 3 ways

It can also be calculated using

C(3,1)=(3 1)=3!/(1!(3−1)!)

where n = 3 and r = 1

C(3,1)=(3 1)=3!/(1!(3−1)!) = 3!/(1!(2)!)= 3*2!/ 1!*2! = 2

Therefore no of ways of not selecting multiple of 2 and 3 is 3 ways

probability of not selecting a multiple of 2 or a multiple of 3 = no of ways of not selecting multiple of 2 and 3 /No of ways of selecting one number out of one to 10 = 3/10 = 0.3

User Jino Shaji
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