MATH SOLVE

4 months ago

Q:
# A jar of alphabet tiles contains 10 unique consonant tiles and 5 unique vowel tiles.If 5 tiles are picked randomly, the probability that 3 are consonants and 2 are vowels is .

Accepted Solution

A:

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 = 10Number of unique vowel tiles = 5Total number of tiles = 10+5=15we need to pick 5 tiles randomly,So, Probability that 3 are consonants and 2 are vowels is given by[tex]\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[/tex]Hence, Probability that 3 are consonants and 2 are vowels is 0.3996.