3.3.1. An urn contains five balls numbered 1 to 5. Two balls are drawn simultaneously. (a) Let X be the larger of the two numbers drawn. Find pX (k). (b) Let V be the sum of the two numbers drawn. Find pV (k).

Step-by-step explanation:

Given that an urn contains five balls numbered 1 to 5

Two balls are drawn simultaneously.

a) X = the larger of two numbers drawn

Assuming balls are drawn without replacement, (since simultaneously drawn)

the sample space would be (1,2) (1,3)(1,4)(1,5) (2,3)(2,4)(2,5) (3,4) (3,5) (4,5)

n(S) = 10

n(x=2) = 1,

n(x=3) =2

n(x=4) = 3

n(x=5) = 4

Larger value  X can take values only as 2,3,4 or 5

X          2              3            4               5

p          0.1           0.2       0.3             0.4

b) V = sum of numbers drawn

V can take values as 3, 4, 5, 6, 7, 8 or 9

V                  3        4             5          6           7             8          9

p                  0.1     0.1         0.2      0.2         0.2        0.1        0.1