(b) 10 draws are made with replacement from the box. What is the probability of

Question

(b) 10 draws are made with replacement from the box. What is the probability of choosing at least 3 vowels? (Note: “Vowels” are the letters A, E, I, O, and U.) Express your answer in the form of a percentage

(c) You make two draws from the box, without replacement. What is the probability that the second draw is an O, given that the first draw was a vowel? Express your answer in the form of a percentage.

4. Consider the box filled with tickets, labelled with the letters shown below (a) 3 tickets are drawn, at random without replacement, from the box. What is the probability of drawing the letters "R, U, N, in that order? Express your answer in the form of a percentage.

Explanation / Answer

there are 7 letters in UNICORN and among this 3 are vowels ( U, I, O) and there are are constant ( N ( two times), C, R)

(a) R can be drawn in first draw with probability 1/7 ,

U can be drawn in second draw with probability 1/6

N can be drawn in third draw with probabiliyt 2/5

required probability of drawing the leterss "R U N"=(1/7)*(1/6)*(2/5)=0.0095=0.95%

(b) proability of drawing of a vowel=3/7 ,

now here we use binomial distribution with parameter n=10 and p=3/7

for Binomial distribution ,P(X=r)=nCrpr(1-p)n-r  

P(at least 3 vowels)=P(X>=3)=1-P(X<=2)=1-0.1255=0.8745=87.45%

(P(X<=2)=0.1255 using ms-excel command =BINOMDIST(2,10,3/7,1))

(c) P( drawing of U or I in first draw )=2/7

P(drawing of O in second draw)=1/6

required probability=(2/7)*(1/6)=1/21=0.0476=4.76%

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