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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’)