A Giant gumball machine contains 10 flavors of gumballs The

A Giant gumball machine contains 10 flavors of gumballs. The gumballs are continually replenished so the 10 flavors are equally distributed. 3 boys and 2 girls each buy one gumball. a) Find the probability that at least two of the children get the same flavor. b) Find the probability that the 2 girls get the same flavor

Solution

Probability that any flavour is selected = 1/10

a. P(at least 2 children get same flavour) = 1 - P(no one gets the same flavour)

P(no one gets the same flavour) = 10*9*8*7*6 / 10⁵ [As 1st person has 10 options, then 2nd has 9 options, and so on, 10⁵ is the total ways of allocating 10 flavours to 5 people]

= 0.3024

P(at least 2 children get same flavour) = 1 - 0.3024 = 0.6976

b. P(2 girls get the same flavour) = (1/10)² *10C1 [As there are 10C1 ways to choose one flavour and both have to get that flavour so (1/10)² ]

= 0.10