84. An urn contains four balls numbered 1, 2, 3, and 4. If two balls are drawn from the urn at random (that is each pair has the same chance of being selected) and Z is the sum of the numbers on the two balls drawn, find (a) the probability distribution of Z and draw a histo- gram; (b) the distribution function of Z and draw its graph.

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Chapter1: Combinatorial Analysis
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Question 84 and 85.

84. An urn contains four balls numbered 1, 2, 3, and 4. If
two balls are drawn from the urn at random (that is, each
pair has the same chance of being selected) and Z is the
sum of the numbers on the two balls drawn, find
(a) the probability distribution of Z and draw a histo-
gram;
(b) the distribution function of Z and draw its graph.
85. A coin is biased so that heads is twice as likely as tails.
For three independent tosses of the coin, find
(a) the probability distribution of X, the total number
of heads;
(b) the probability of getting at most two heads.
Transcribed Image Text:84. An urn contains four balls numbered 1, 2, 3, and 4. If two balls are drawn from the urn at random (that is, each pair has the same chance of being selected) and Z is the sum of the numbers on the two balls drawn, find (a) the probability distribution of Z and draw a histo- gram; (b) the distribution function of Z and draw its graph. 85. A coin is biased so that heads is twice as likely as tails. For three independent tosses of the coin, find (a) the probability distribution of X, the total number of heads; (b) the probability of getting at most two heads.
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