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ProbabilityQ&A Libraryasotherwise.)3 If each voter is for Proposition A with probability .7, what is the probability thatexactly 7 of 10 voters are for this proposition?left-handedness) of a personofgenes,andsuppose that d representeis classified on the basis of one pairdominant gene and r a recessive gene. Thus, a person with dddominance, one with rr is pure recessive, and one with rd is hybrid. Thedominance and the hybrid are alike in appearance. Children receive 1 genc feeach parent. If, with respect to a particular trait, 2 hybrid parents have a toralof 4 children, what is the probability that 3 of the 4 children have the outwardgenes ispurepureappearance of the dominant gene?5. At least one-half of an airplane's engines are required to function in order for irto operate. If each engine independently functions with probability p, for wharvalues of p is a 4-engine plane more likely to operate than a 2-engine plane?6. Let X be a binomial random variable withE[X] =7__and Var(X) = 2.1Find(a) P{X = 4};(b) P{X> 12}.%3D7. If X and Y are binomial random variables with respective parameters (n, p) and(n, 1- p), verify and explain the following identities:(a) P{X < i} = P{Y >n- i};(a) P{X = k} = P{Y = n- k).8. If X is a binomial random variable with parameters n%3D%3D%3D%3DandP,where 0 < p < l,Question

Asked Feb 5, 2020

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Question 3

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**Binomial distribution:**

The binomial distribution gives the probability of number of successes out of *n* trials in a series of Bernoulli trials.

The probability mass function (pmf) of a binomial random variable *X* is given as:

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