Two balls are drawn at random with replacement from a box containing $10$ black and $8$ red balls. Find the probability that One of them is black and other is red.
Two balls are drawn at random with replacement from a box containing $10$ black and $8$ red balls. Find the probability that One of them is black and other is red.
Total number of balls $=18$
Number of red balls $=8$
Number of black balls $=10$
Probability of getting first ball as red $=\frac{8}{18}=\frac{4}{9}$
The ball is replaced after the first draw.
Probability of getting second ball as black $=\frac{10}{18}=\frac{5}{9}$
Therefore, probability of getting first ball as black and second ball as red $=\frac{4}{9} \times \frac{5}{9}=\frac{20}{81}$
Therefore, probability that one of them is black and other is red
$=$ Probability of getting first ball black and second as red $+$ Probability of getting first ball red and second ball black
$=\frac{20}{81}+\frac{20}{81}$
$=\frac{40}{81}$
Similar Questions
Let $A$,$B$ and $C$ be three events such that $P\left( {A \cap \bar B \cap \bar C} \right) = 0.6$, $P\left( A \right) = 0.8$ and $P\left( {\bar A \cap B \cap C} \right) = 0.1$, then the value of $P$(atleast two among $A$,$B$ and $C$ ) equals
Let $A$,$B$ and $C$ be three events such that $P\left( {A \cap \bar B \cap \bar C} \right) = 0.6$, $P\left( A \right) = 0.8$ and $P\left( {\bar A \cap B \cap C} \right) = 0.1$, then the value of $P$(atleast two among $A$,$B$ and $C$ ) equals
Two cards are drawn at random and without replacement from a pack of $52$ playing cards. Finds the probability that both the cards are black.
Two cards are drawn at random and without replacement from a pack of $52$ playing cards. Finds the probability that both the cards are black.
If $A$ and $B$ are any two events, then the probability that exactly one of them occur is
If $A$ and $B$ are any two events, then the probability that exactly one of them occur is
- [IIT 1984]
The probability of solving a question by three students are $\frac{1}{2},\,\,\frac{1}{4},\,\,\frac{1}{6}$ respectively. Probability of question is being solved will be
The probability of solving a question by three students are $\frac{1}{2},\,\,\frac{1}{4},\,\,\frac{1}{6}$ respectively. Probability of question is being solved will be
The probabilities that $A$ and $B$ will die within a year are $p$ and $q$ respectively, then the probability that only one of them will be alive at the end of the year is
The probabilities that $A$ and $B$ will die within a year are $p$ and $q$ respectively, then the probability that only one of them will be alive at the end of the year is