Question

Mr. Garcia has 15 boys and 10 girls in his math class. He selects two students at random to demonstrate how they solved the day’s challenge assignment. What is the probability that both students are girls?

Answer 1

Answer: $\frac{3}{20}$

Step-by-step explanation:

Since, the number of boys = 15

The number of girls = 10

Total number of students = 15 + 10 = 25

Thus, If two students are chosen then the probability that both are girls

$=\frac{^{10}C_2}{^{25}C_2}$

$=\frac{\frac{10!}{2!(10-2)!}}{\frac{25!}{2!(25-2)!}}$

$=\frac{\frac{10\times 9\times 8!}{2!8!}}{\frac{25\times 24\times 23!}{2!23!}}$

$=\frac{5\times 9}{25\times 12}$

$=\frac{45}{300}$

$=\frac{3}{20}$

Hence, the required probability is 3/20.

Answer 2

The probability that both students are girls is 3/20 or 0.15 if Mr. Garcia has 15 boys and 10 girls in his math class. He selects two students at random to demonstrate how they solved the day’s challenge assignment.

What is probability?

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

We have:

Total number of boys in Garcia's math class = 15

Total number of girls in Garcia's math class = 10

Total number of students = 15+10 ⇒ 25

Total number of outcomes = $_{25}^{}\textrm{C}_2$

Total number of favorable outcomes = $_{10}^{}\textrm{C}_2$

Now, the probability,

$=\rm \frac{_{10}^{}\textrm{C}_2}{_{25}^{}\textrm{C}_2}$

The value of $_{25}^{}\textrm{C}_2 = 300$

The value of $_{10}^{}\textrm{C}_2 =45$

$=\frac{45}{300}$

= 3/20 or 0.15

Thus, the probability that both students are girls is 3/20 or 0.15 if Mr. Garcia has 15 boys and 10 girls in his math class. He selects two students at random to demonstrate how they solved the day’s challenge assignment.

Learn more about the probability here:

brainly.com/question/11234923

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