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?
given: 20 cards numbered from 1-20
formula:
one card is drawn at random therefore total possible outcomes are 20C1
therefore n(S)=20C1=20
(i) let E be the event that the number on the drawn card is a multiple of 4
E= {4, 8, 12, 16, 20}
n(E)= 5C1=5
(ii) let E be the event that the number on the drawn card is not a multiple of 4
E’ be the event that the number on the drawn card is a multiple of 4
E’= {4, 8, 12, 16, 20}
n(E)= 5C1=5
P(E)=1-P(E’)
(iii) let E be the event that the number on the drawn card is odd
E= {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}
n(E)= 10C1=10
(iv) let E be the event that the number on the drawn card is greater than 12
E= {13, 14, 15, 16, 17, 18, 19, 20}
n(E)= 8C1=8
(v) let E be the event that the number on the drawn card is a multiple of 5
E= {5, 10, 15, 20}
n(E)= 4C1=4
(vi) let E be the event that the number on the drawn card is not divisible by 6
let E’ be the event that number on the drawn card is divisible by 6
E’= {6, 12, 18}
n(E’)= 3C1=3
P(E)=1-P(E’)