Question

In: Statistics and Probability

Suppose that there are two hats in front of you. Hat 1 contains 4 green balls...

Suppose that there are two hats in front of you.

  • Hat 1 contains 4 green balls and 6 orange balls.

  • Hat 2 contains 3 green balls, 6 orange balls, and a purple ball.

  • (a) Suppose you draw one ball from each hat. The outcome of interest is the colour of each of the drawn balls. How many elements are in the sample space of this experiment?

  • (b) Write out the complete sample space for the experiment above.

  • (c) What is the probability that you draw two balls of the same colour?

(d) Consider the following variables.

  • Suppose you draw from Hat 1, without replacement, until you get a green ball. Let X be the number of draws until you get a green ball.

  • Suppose you draw a ball from Hat 1 and a ball from Hat 2. Let Y be the number of drawn orange balls.

  • Suppose you draw a ball from Hat 1 and a ball from Hat 2. Let Z be the number of drawn green balls.

  • Suppose you draw 6 balls from Hat 2, with replacement. Let W be the number of times a green ball is drawn.

    Determine which of the above variables follow a binomial distribution. Also, for each binomially-distributed variable, determine the parameters n and p.

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Expert Solution

orchestra answered 1 year ago
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