Question

PLEASE HELP ME OUT ASAP

Answer 1

Since the tiles are not (assumed) replaced, binomial distribution does not apply.

The problem can be solved by either

1. considering combinations and permutations

2. the hypergeometric distribution.

The latter will be used because it is simple.

Use hypergeometric distribution where:

a=number of consonants selected

A=total number of consonants

b=number of vowels selected

B=total number of vowels

Then

`P(a,b)=(C(A,a)C(B,b))/(C(A+B,a+b))`

where

`C(n,r)=(n!)/((n!(n-r)!))` = combination of r items selected from n,

A+B=total number of tiles

a+b=number of tiles selected

For a=3, b=2, A=10, B=5

`P(a,b)=(C(A,a)C(B,b))/(C(A+B,a+b))`

`P(3,2)=(C(10,3)C(5,2))/(C(15,5))`

`=(C(10,3)C(5,2))/(C(15,5))`

`=(120*10)/(3003)`

`=(400)/(1001)`

=0.3996 (to four decimal places)