A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?

Question

A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?

$$\frac{{4}}{{9}}$$
$$\frac{{5}}{{9}}$$
$$\frac{{7}}{{9}}$$
$$\frac{{8}}{{9}}$$

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AhmedNazir · Answer 1 · Sep 01, 2022 13:21:41

Answer: Option 2

Two balls can be picked from nine balls in $${{}^9{C_2}}$$ ways. We select one white ball and one red ball from five white balls and four red balls. This can be done $${{}^5{C_1}}$$ . $${{}^4{C_1}}$$ ways. ∴ The required probability $$\eqalign{ & = \frac{{5 \times 4}}{{{}^9{C_2}}} \cr & = \frac{{20}}{{36}} \cr & = \frac{5}{9} \cr} $$

A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?

1 Answers