Question

Five balls, numbered 1, 2, 3, 4, and 5, are placed in an urn. Two balls are randomly selected from the five, and their numbers noted. Find the probability distribution for the following: a The largest of the two sampled numbers b The sum of the two sampled numbers

Answer 1

Answer

given,

five balls numbered 1, 2, 3, 4, and 5.

two balls are drawn randomly

number of ways of selecting two balls = ⁵C₂ = 10 ways

For sample to be of largest number there is two option 4 or 5

so for first section of ball probability will be = $\dfrac{2}{5}$

now one ball is selected so for the selection of second ball the ball are 4

probability of second ball selection = $\dfrac{1}{4}$  

a) largest of the two sample

               = $\dfrac{2}{5}\times \dfrac{1}{4}$

               = $\dfrac{1}{10}$

               =0.1

b) sum of two sample

               =  $\dfrac{2}{5}+\dfrac{1}{4}$  

               = $\dfrac{13}{20}$

               = 0.65