A letter is drawn 1,000 times, at random, from the word A R AB I A. There are tw

Question

A letter is drawn 1,000 times, at random, from the word A R AB I A. There are two offers. (A) You win a dollar if the number of A's among the draws is10 or more above the expected number. (B) You win a dollar if the number of B's among the drawsis 10 or more above the expected number.
Choose one option and explain. (i) A gives a better chance of winning than B. (ii) A and B give the same chance of winning. (iii) B gives better chance of winning than A. (iv) There is not enough information to decide.
A letter is drawn 1,000 times, at random, from the word A R AB I A. There are two offers. (A) You win a dollar if the number of A's among the draws is10 or more above the expected number. (B) You win a dollar if the number of B's among the drawsis 10 or more above the expected number.
Choose one option and explain. (i) A gives a better chance of winning than B. (ii) A and B give the same chance of winning. (iii) B gives better chance of winning than A. (iv) There is not enough information to decide.

Explanation / Answer

P(A)=3/6=1/2=p is probability of drawing an A on a draw.Probability of not gettin an a is .5=q mean of binominal =np=1000(.5)=500, variance of binomial=(npq)=250=15.81 let x be the number of A's in 1000 draws. P(x>510) is required, I will approximate binomial distribution xwith u a normal distribution with the same mean and variance. P(x>510)=P(u>509.5)=P(z>(509.5-500)/15.81)=P(z>.6)=.5-P(0176.67)= P(v>176.5)= P((v-166.67)/11.76>(176.5-166.67)/11.76)=P(z>.84)=.5-P(0

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