Question

Suppose that a class contains 15 boys and 30 girls, and that 10 students are to be selected at random for a special assignment. Find the probability that exactly 3 boys will be selected.

Answer 1

Here, I'll use C for combinations.
There are 15 boys and you need 3 so 15 C 3 ways
There are 30 girls and you need 7 so 30 C 7
and there are 45 total and you need 10 so 45 C 10

The answer is [15 C 3 • 30 C 7] over 45 C 10

so do that on your calculator if you need an actual decimal.

Answer 2

The probability that exactly 3 boys will be selected is 0.29.

What is probability?

The term probability can be defined as the chance of happening an event or incident.

Here, a class contains 15 boys and 30 girls.

Therefore, total students are 45.

10 students are to be selected at random and there must be exactly 3 boys.

Therefore, there are 3 boys and 7 girls in that selected group.

Now, 3 boys can be selected from 15 boys in ways

= $C_{3} ^{15}$

= 455

Again, 7 girls can be selected from 30 girls in ways

= $C_{7} ^{30}$

= 2035800

Now, 10 students can be selected among 45 students is

= $C_{10} ^{45}$

= 3190187286

Therefore, the required probability is

= ($C_{3} ^{15}$ × $C_{7} ^{30}$) / $C_{10} ^{45}$

= (455 × 2035800)/3190187286

= 0.29

Learn more about probability here: https://brainly.com/question/21653695

#SPJ2