Question

The word geometry has eight letters. three letters are chosen at random. what is the probability that two consonants and one vowel are chosen? 0.536 0.268 0.179 0.089

Answer 1

Answer:

0.536 is the required probability.

Step-by-step explanation:

 We have been given the word the word "GEOMETRY"

we have to find the probability that two consonants and one vowel are chosen:

Number of consonants are: 5

Number of  vowels are: 3

Hence, The required probability is: $\frac{^5C_2\cdot ^3C_1}{^8C_3}$

Using: $^nC_r=\frac{n!}{(r!)(n-r)!}$

$\frac{\frac{5!}{3!\cdot 2!}\cdot\frac{3!}{1!\cdot 2!}}{\frac{8!}{3!\cdot 5!}}$

Simplifying the above expression:

$\frac{\frac{5\cdot 4\cdot 3!}{3!\cdot 2}\cdot {\frac{3\cdot 2!}{2!}}}{\frac{8\cdot 7\cdot 6\cdot 5!}{5!\cdot 3\cdot 2}}$

Further simplification after cancelling out the common terms we get:

$\Rightarrow \frac{30}{56}=\frac{15}{28}=0.5357=0.536$

Hence, Option 1 is correct.

Answer 2

The probability helps us to know the chances of an event occurring. The probability that two consonants and one vowel are chosen is 0.536.

What is Probability?

The probability helps us to know the chances of an event occurring.

$\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}$

Given the word Geometry has 8 letters. Therefore, the number of consonants in the word is 5, while the number of vowels is 3.

Now, the number of cases when the two consonants and vowels can be chosen are:

$\text{Number of cases} = ^5C_2 \times ^3C_1 = 10 \times 3 = 30$

The total number of cases will be

$\text{Number of cases} = ^8C_3 = 56$

Now,  the probability that two consonants and one vowel are chosen can be written as,

$\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}$

$\rm Probability=\dfrac{30}{56} = 0.536$

Hence, the probability that two consonants and one vowel are chosen is 0.536.

Learn more about Probability:

https://brainly.com/question/795909

#SPJ3