Suppose there are three balls in a box. On one of the balls is the number 1, on another is the number 2, and on the third is the number 3. You select two balls at random and without replacement from the box and note the two numbers observed. The sample space S consists of the three equally likely outcomes ((1,2), (1,3), (2,3)) (disregarding order). Let X be the sum of the two balls selected. (a) What is the distribution for X? (b) What is the probability that the sum is at least 4? (c) What is the mean of X?

Question

Jacob Davis

Mathematics

6 February, 01:27

Suppose there are three balls in a box. On one of the balls is the number 1, on another is the number 2, and on the third is the number 3. You select two balls at random and without replacement from the box and note the two numbers observed. The sample space S consists of the three equally likely outcomes ((1,2), (1,3), (2,3)) (disregarding order). Let X be the sum of the two balls selected. (a) What is the distribution for X? (b) What is the probability that the sum is at least 4? (c) What is the mean of X?

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Alyssa Owen · Answer 1

Step-by-step explanation:

a) X is a discrete uniform distribution. As the number of outcomes is only 3.

b) sum is at least 4

X ≥ 4

i. e (1,3) or (2,3)

probability of X ≥ 4 is 2/3

2/3 = 0.667

66.7 % is the probability of the outcome to have a sum at least 4.

c) The 3 likely outcome of X

(1,2) where X; 1+2=3

(1,3) where X; 1+3=4

(2,3) where X; 2+3=5

Mean = 3+4+5 / 3

Mean = 4

Feel free to ask any uncleared step