Question

An urn contains 17 white balls and 18 red balls. A sample of four balls is selected at random from the urn. What is the probability that the sample contains two white balls and two red ones?

a. 0.0286
b. 0.2286
c. 0.3974
d. 0.0944
e. 0.0442
f. None of the above.

Answer 1

Answer:

c. 0.3974

Step-by-step explanation:

Given;

number of white balls, W = 17

number of red balls, R = 18

Total number of balls, T = 35

The number of ways the event will occur is given by

= P(2 whites) and P(2 reds)

= P(2whites) x P(2 reds)

= 17C2 x 18C2

= 136 x 153

= 20,808

The total number of possible outcome

= 35C4

= 52,360

The probability = 20,808 / 52,360

                          = 0.3974

The correct option is "C"

Answer 2

Probability that the sample contains two white balls and two red ones is equal to 0.3974.

So, option c. is correct.

Permutations and combinations

Probability is a discipline of mathematics concerned with numerical explanations of the likelihood of an event occurring or the truth of a claim.

Number of white balls $=\boldsymbol{17}$

Number of red balls $=\boldsymbol{18}$

Total number of balls $=\boldsymbol{35}$

Probability that the sample contains two white balls and two red ones  

$=\frac{\binom{17}{2}\binom{18}{2}}{\binom{35}{4}}$

$=\frac{\frac{17!}{15!2!}\frac{18!}{16!2!}}{\binom{35!}{31!4!}}$

$=\boldsymbol{0.3974}$

So, option c. is correct.

Find more information about combinations here:

https://brainly.com/question/815369?referrer=searchResults