Question

A bag contains 15 cards with 1 – 15 numbers written on it. Find the probability of picking a card that is an even number or a multiple of 3.

Answer 1

2/3

Explanation:

Even numbers are 2,4,6,8,10,12,14

Multiple of 3 ( other than 6,12 ) are 3,9,15

P=10/15 (simplify by 5)

P=2/3

Answer 2

Explanation:

Given

No of sample space , n(s)= 15

Even numbers = ( 2 , 4 , 6 , 8 , 10 ,12 , 14 )

No of favorable cases of getting even numbers , n(a)= 7

Now

Multiples of 3 = ( 3, 6 , 9 , 14, 15 )

No of favorable cases of multiples of 3 , n(b) = 5

Now

n ( a ∩ b)= 2

Now Probability of picking a card that is an even number or a multiple of 3

P( a U b) or

P( a or b)

= P(a) + P(b) - P( a ∩ b )

= n(a)/ n(s) + n(b) / n(s) - n( a∩ b) / n(s)

= 7 / 15 + 5 / 15 - 2/15

= ( 7 + 5 - 2) / 15

= 10 / 15

= 2 / 3

Hope it helps :)