Question

A jar of alphabet tiles contains 10 unique consonant tiles and 5 unique vowel tiles.

Answer 1

Answer: Probability that 3 are consonants and 2 are vowels is 0.3996.

Step-by-step explanation:

Since we have given that

Number of unique consonant tiles = 10

Number of unique vowel tiles = 5

Total number of tiles = 10+5=15

we need to pick 5 tiles randomly,

So, Probability that 3 are consonants and 2 are vowels is given by

$\frac{^{10}C_3\times ^5C_2}{^{15}C_5}\\\\=\frac{\frac{10\times 9\times 8}{3\times 2\times 1}\times \frac{5\times 4}{2\times 1}}{\frac{15\times 14\times 13\times 12\times 11}{5\times 4\times 4\times 3\times 2\times 1}}\\\\=0.3996$

Hence, Probability that 3 are consonants and 2 are vowels is 0.3996.

Answer 2

Answer:

$\bf\text{The required probability = }\frac{400}{1001}$

Step-by-step explanation:

This problem can easily be solved by using Hyper geometric Distribution :

Total number of tiles, N = 15

Number of tiles picked, n = 5

Number of successes, initially , k = 10

Number of successes for which to find, r = 3

Now, we need to calculate P(r = 3)

$\implies P(r = 3)=\frac{_r^n\txterm C \times _{k-r}^{N-n}\txterm C}{_k^N\txterm C}\\\\ \implies P(r=3)=\frac{_3^5\txterm C \times _{7}^{10}\txterm C}{_{10}^{15}\txterm C}\\\\ \implies P(r=3)=10\times\frac{120}{3003}\\\\\implies P(r=3)=\frac{400}{1001}$

$\bf\text{Hence, The required probability = }\frac{400}{1001}$