20 cards are numbered from 1 to 20. One card is drawn at random. What is the probability that the number on the cards is:
(i) a multiple of 4?
(ii) not a multiple of 4?
(iii) odd?
(iv) greater than 12?
(v) divisible by 5?
(vi) not a multiple of 6?
We have 20 cards numbered from 1 to 20, one card is drawn at random
∴n(s)=20C1=20
(i) Let E be the event that the number on the drawn cards is multiple of 4
∴E={4,8,12,16,20}
∴n(E)=5
∴P(E)=520=14
(ii) Let E be the event that the number on the drawn card is not the multiple of 4
∴˜E be the event that the number on the drawn card is the multiple of 4
∴˜E{4,8,12,16,20}
⇒˜E=520=14
∴P(E)=1−∴P˜E
=1−14=34
(iii) Let E be the event that the number of the drawn card is odd.
∴E={1,3,5,7,9,11,13,15,17,19}
∴n(E)=10
∴P(E)=1020=12
(iv) Let E be the event that number on the drawn card is greater that 12.
∴E={13,14,15,16,17,18,19,20}
∴n(E)=8
⇒P(E)=820=25
(v) Let E be the event that number on the drawn card is divisible by 6.
E=(5,10,15,20)
n(E)=4
∴P(E)=420=15
(vi) Let E be the event that number on the drawn card is not divisible by 6.
∴˜E be the event that number on the drawn card is divisible by 6
∴˜E={6,12,18}
⇒n(˜E)=3
∴P(˜E)=320
P(E)=1−P(˜E)
=1−320=1720