Tag Archives: Mixed Distribution

Exam P Practice Problem 108 – random selection of balls

Both 108-A and 108-B use the following information.

Bowl One contains 1 blue ball and 4 orange balls. Bowl Two contains 3 blue balls and 2 orange balls. A bowl is chosen at random. Balls are randomly chosen one at a time from the chosen bowl, with each chosen ball returning to the bowl.

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Problem 108-A

What is the probability that four of the first six selections are blue ball?

      \displaystyle \bold ( \bold A \bold ) \ \ \ \ \ \ \ \ \ \ \ \  \frac{\bold 4 \bold 8 \bold 6}{\bold 3 \bold 1 \bold 2 \bold 5}

      \displaystyle \bold ( \bold B \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \frac{\bold 1 \bold 0 \bold2}{\bold 6 \bold 2 \bold 5}

      \displaystyle \bold ( \bold C \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \frac{\bold 3 \bold 4}{\bold 2 \bold 0 \bold 5}

      \displaystyle \bold ( \bold D \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \frac{\bold 2 \bold 1}{\bold 1 \bold 2 \bold 5}

      \displaystyle \bold ( \bold E \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \frac{\bold 1 \bold 0 \bold 2 \bold 0}{\bold 3 \bold 1 \bold 2 \bold 5}

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Problem 108-B

If four of the first six selections are blue balls, what is the probability that the balls are selected from Bowl One?

      \displaystyle \bold ( \bold A \bold ) \ \ \ \ \ \ \ \ \ \ \ \  \frac{\bold 9}{\bold 2 \bold 5 \bold 5}

      \displaystyle \bold ( \bold B \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \frac{\bold 2}{\bold 4 \bold 3}

      \displaystyle \bold ( \bold C \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \frac{\bold 4}{\bold 8 \bold 5}

      \displaystyle \bold ( \bold D \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \frac{\bold 1 \bold 5}{\bold 2 \bold 5 \bold 5}

      \displaystyle \bold ( \bold E \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \frac{\bold 1}{\bold 2}

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Answers

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Exam P Practice Problem 86 – Finding Mean and Variance

The following is the cumulative distribution function of the random variable X.

    \displaystyle F(x)=\left\{\begin{matrix} \displaystyle 0&\ \ \ \ \ \ x < 0 \\{\text{ }}& \\{\displaystyle \frac{(x+2)^2}{100}}&\ \ \ \ \ \ 0 \le x <6 \\{\text{ }}& \\{\displaystyle 1}&\ \ \ \ \ \ 6 \le x <\infty  \end{matrix}\right.

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Problem 86-A

Calculate the expected value of X.

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \   2.16

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \   3.35

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \   4.32

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \   6.00

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \   6.67

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Problem 86-B

Calculate the variance of X.

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 3.240

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 3.658

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 3.957

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 4.694

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 5.556

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