Matematika a letter is selected at random from each of the word 'NICE' and 'ICE'
represent the sample space using a possibility diagram and find the probability two letters are the same and the vowels!​

a letter is selected at random from each of the word 'NICE' and 'ICE'
represent the sample space using a possibility diagram and find the probability two letters are the same and the vowels!​

Jawaban:

Correct options are A) , B) and C)

(A) Total number of letters in the given word = 4, out of these O and E are two vowels.

Let S be the sample space, then

S={HO,HM,HE,OM,OE,ME}⇒n(S)=6

Let A1 be the event of taking two vowels, then 

A1={OE}=n(S)n(A1)=61

(B) Let A2 be the event of taking at least one vowel, then we have

A2={HO,HE,OE,ME,MO}⇒n(A2)=5

Hence, required probability =n(S)(n(A2))=65

(C) Let A3 be the event of taking one letter as M, then we have A3={HM,OM,ME}⇒n(A2)=5

Hence,required probability =n(S)n(A3)=63=21

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