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13 votes
a. A contest entrant has a 0.002 probability of winning $12,165. If this is the only prize and the fee is $35, then find the expected value of winning the contest. b. The probability of winning a lottery is 0.125. What is the probability of winning AT LEAST ONCE in twelve trials?

User Giordanolima
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1 Answer

24 votes
24 votes

Answer:

The right answer is:

(a) -10.67

(b) 0.7986

Explanation:

(a)

According to the question,

X P(X) X.P(X) X2.P(X)

12130 0.002 24.26 294274

-35 0.998 -34.93 1222.55

Now,


\Sigma x.P(x) = -10.67

or,


\Sigma x^2.P(x) = 295496.35

hence,

The mean will be:


\Sigma x.P(x) = -10.67

(b)

According to the question,

n = 12

p = 0.125

q = 1 - p

= 0.875

Now,


P(X=x) = \binom{n}{x} p^x q^(n-x)

By substituting the values, we get


P(X \geq 1)=1-(\binom{12}{0} 0.125^0. 0.875^(12-0))


=1-(1 (0.125^0) (0.875^(12)))


=1-(1(1.0)(0.2014))


=1-(0.2014)


=0.7986

User Zzn
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