Question

Two balls are drawn at random from an urn containing six white and nine red balls. Recall the equatio n for an. r) given below. C(n,r) (a) Use combinations to compute the probability that both balls are white. (b) Compute the probability that both balls are red. (a) The probability that both balls are white is (Type an integer or a decimal. Round to two decimal places as needed.)

Answer 1

Answer: (a)  $\dfrac{1}{7}$    (b)  $\dfrac{12}{35}$

Step-by-step explanation:

Given: Number of white balls : 6

Number of red balls = 9

Total balls = 15

(a)  The probability that both balls are white is given by :-

$\dfrac{^6C_2}{^{15}{C_2}}\\\\=\dfrac{\dfrac{6!}{2!(6-2)!}}{\dfrac{15!}{2!(15-2)!}}=\dfrac{1}{7}$

∴ The probability that both balls are white is  $\dfrac{1}{7}$ .

(b)  The probability that both balls are red is given by :-

$\dfrac{^9C_2}{^{15}C_2}\\\\=\dfrac{\dfrac{9!}{2!(9-2)!}}{\dfrac{15!}{2!(15-2)!}}=\dfrac{12}{35}$

∴ The probability that both balls are red is $\dfrac{12}{35}$ .