Can you please include a brief explanation Consider the foll

Can you please include a brief explanation?

Consider the following experiment: Rolling a pair of fair dice 10 times and recording the number of times we get a 7. 8. One of the following statements is not true. a) A fixed number of trials. 10 b) The probability of rolling a 7 is 1/6 for every trial. c) There are several possible outcomes. d) Each trial is independent. 9. The probability of rolling exactly 3 sevens is: a) 0.8450 b) 0.8965 c) 0.1550 d) 01035 10. The probability of rolling at least 1 seven. a) 0.8385 5)0.1615 c) 0.0985 d)0.9015

Solution

(8)C

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(9)Given X follows Binomial distribution with n=10 and p=1/6

P(X=x)=10Cx*(1/6)^x*(5/6)^(10-x) for x=0,1,2,...,10

So the probability is

P(X=3) =10C3*(1/6)^3*(5/6)^(10-3) =0.1550454

Answer: c

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(10)P(X>=1) = 1-P(X=0)

=1-10C0*(1/6)^0*(5/6)^(10-0)

=0.8384944

Answer: A