Cards marked with numbers 5,6,7.......30 are placed in a box and mixed thoroughly and one card is drawn at random from the box. What is the probability that the number on the card is

i) a prime number ?

ii) a multiple of 3 or 5 ?

iii) neither divisible by 5 nor by 10?

Total number of cards = 30-5+1=26

i) prime={ 7,11,13,17,19,23,29}  (total =7)
Probability= 7/26

ii) Numbers which are divisible by 3 or 5 ={3,5,6,9,10, 12,15,18,20, 21, 24,25,27,30} (total:14)

Probability=14/26=7/13

iii) neither divisible by 5 nor by 10
={6,7,8,9,11,12,13,14,16,17,18,19,21,22,23,24,26,27,28,29} (total: 20)
Probability= 20/26= 10/13

  • 2
P(E)=FAV OUTCOME/POSSIBLE OUTCOME

{A}possibleoutcome=25

prime= 7,11,13,17,19,23,29,=7

p(e)=7/25

{B}multiple of 3/5=13 (ie6, 9, 12,15 ,21, 24,27,30,5, 10,20 ,25,)

p(e)=13/25

{C}neither divisible by 5/10 in this case we need to first find divisible by 5/10 = 5,10, 15,20, 25, 30 =6

p(divisibleby 5/10)=6/25

p(not e)= 1-p(E) = 1 - 6/25 = 19/25

  • -4

P(E)=FAV OUTCOME/POSSIBLE OUTCOME

{A}possibleoutcome=25

prime= 7,11,13,17,19,23,29,=7

p(e)=7/25

{B}multiple of 3/5=13 (ie6, 9, 12,15 ,21, 24,27,30,5, 10,20 ,25,)

p(e)=13/25

{C}neither divisible by 5/10 in this case we need to first find divisible by 5/10 = 5,10, 15,20, 25, 30 =6

p(divisibleby 5/10)=6/25

p(not e)= 1-p(E) = 1 - 6/25 = 19/25

  • -2
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