A component may come from any one of three manufacturers with probabilities p1=0.25,p2=0.50,and p3=0.25. The probabilities that the components will function properly are a function of the manufacturer and are 0.1, 0.2, and 0.4 for the first, second, and third manufacturer, respectively. a. Compute the probability that a randomly chosen component will function properly. b. Compute the probability that three components in series randomly selected will function properly

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A component may come from any one of three manufacturers with probabilities p1=0.25,p2=0.50,and p3=0.25. The probabilities that the components will function properly are a function of the manufacturer and are 0.1, 0.2, and 0.4 for the first, second, and third manufacturer, respectively.  a. Compute the probability that a randomly chosen component will function properly.  b. Compute the probability that three components in series randomly selected will function properly

Archie Jones · Accepted Answer

Step 1 Given that: Probabilities of coming from the 3 manufacturers are respectively: p1=0.25,p2=0.5,p3=0.25 Probabilities that the components coming from manufacturers function properly are: p(m1)=0.1,p(m2)=0.2,p(m3)=0.4 a) Therefore, the probability that a randomly chosen component will function properly is: P=p1×p(m1)+p2×p(m2)+p3×p(m3) =0.25×0.1+0.5×0.2+0.25×0.4 =0.225 Step 2 b) Let X be the number of components randomly selected that function properly. Then, X∼Binomial(n=3,p=0.225) with probability density function as: P(X=x)=nCx×px(1−p)n−x;x=0,1,2,3 Therefore, Probability that 3 components selected function property is: P(X=3)=3C3×(0.225)3(1−0.225)3−3 =0.01139

MoxboasteBots5h · Accepted Answer

Step 1  Given a probability distribution, you can find cumulative probabilities. For example, the probability of getting 1 or fewer heads [P(X≤1)] is P(X=0)+P(X=1), which is equal to 0.25+0.50or0.75.  The probability distribution of a continuous random variable is represented by an equation, called the probability density function (pdf). All probability density functions satisfy the following conditions:  The random variable Y is a function of X; that is, y=f(x).  The value of y is greater than or equal to zero for all values of x.  The total area under the curve of the function is equal to one.  The charts below show two continuous probability distributions. The first chart shows a probability density function described by the equation  y=1  over the range of 0 to 1 and  y=0  elsewhere. The second chart shows a probability density function described by the equation  y=1−0.5x  over the range of 0 to 2 and  y=0  elsewhere. The area under the curve is equal to 1 for both charts.  The probability that a continuous random variable falls in the interval between a and b is equal to the area under the pdf curve between a and b.   For example, in the first chart above, the shaded area shows the probability that the random variable X will fall between 0.6 and 1.0.   That probability is 0.40. And in the second chart, the shaded area shows the probability of falling between 1.0 and 2.0. That probability is 0.25.

A component may come from any one of three manufacturers wit

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