Question:
A bag contains $6$ red, $5$ blue and $7$ white balls. If three balls are drawn one by one (without replacement), then what is the probability that all three balls are blue?
A bag contains $6$ red, $5$ blue and $7$ white balls. If three balls are drawn one by one (without replacement), then what is the probability that all three balls are blue?
Updated On: Jul 5, 2022
- $\frac{3}{204}$
- $\frac{7}{408}$
- $\frac{5}{204}$
- $\frac{5}{408}$
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Let $A$, $B$ and $C$ be events of drawing a red ball in first, second and third draw respectively. Then probability of getting red ball in all three draws
$P (A \,\cap\, B \,\cap C ) = P(A). P(B|A). P(C|A\,\cap\,B)$
Now, $P(A) = \frac{5}{18}$, $P(B| A) = \frac{4}{17}$
and $P (C |A \cap B ) =\frac{3}{16}$
$\therefore P(A \cap B \cap C) = P(A).P(B|A).P(C|A \cap B)$
$=\frac{5}{18} \times \frac{4}{17} \times \frac{3}{16}$
$= \frac{5}{408}$
Was this answer helpful?
0
0
Top Questions on Conditional Probability
- If \( P(A|B) = P(A'|B) \), then which of the following statements is true?
- CBSE CLASS XII - 2024
- Mathematics
- Conditional Probability
- \(\text{Let } X \text{ denote the number of hours you play during a randomly selected day. The probability that } X \text{ can take values } x \text{ has the following form, where } c \text{ is some constant:}\)
\(P(X = x) = \begin{cases} 0.1, & \text{if } x = 0 \\ cx, & \text{if } x = 1 \text{ or } x = 2 \\ c(5 - x), & \text{if } x = 3 \text{ or } x = 4 \\ 0, & \text{otherwise} \end{cases}\)
\(\text{Match List-I with List-II:}\)
- CUET (UG) - 2024
- Mathematics
- Conditional Probability
- The probability that a student passes only in Mathematics is \(\frac{1}{3}\).The probability that the student passes only in English is \(\frac{4}{9}\).The probability that the student passes in both of these subjects \(\frac{1}{6}\).The probability that the student will pass in at least one of these two subjects is
- GATE CE - 2024
- Mathematics
- Conditional Probability
- If $A$ and $B$ are two events such that $P ( A )=\frac{1}{3}, P ( B )=\frac{1}{5}$ and $P ( A \cup B )=\frac{1}{2}$, then $P \left( A \mid B ^{\prime}\right)+ P \left( B \mid A ^{\prime}\right)$ is equal to
- JEE Main - 2023
- Mathematics
- Conditional Probability
- If A and B are events such that P(A)=\(\frac{1}{4}\), P(A/B)=\(\frac{1}{2}\) and P(B/A)=\(\frac{2}{3}\) then P(B) is
- KCET - 2023
- Mathematics
- Conditional Probability
View More Questions
Notes on Conditional Probability
Concepts Used:
Semiconductors
Semiconductors are a crystalline solid materials, whose electrical conductivity lies between a conductor and an insulator. Semiconductors are mainly used in the manufacturing of electronic devices like capacitors, transistors, diodes, Integrated circuits, etc.
Properties of Semiconductor:
- Semiconductor acts like an insulator at Zero Kelvin. On increasing the temperature, it works as a conductor.
- Due to their exceptional electrical properties, semiconductors can be modified by doping to make semiconductor devices suitable for energy conversion, switches, and amplifiers.
- Lesser power losses.
Uses of Semiconductor:
- Semiconductors are widely used in manufacturing electronics devices like transistors, diodes, sensors, integrated circuits.
- Semiconductors are widely used in all electronic devices, like mobile phones, digital cameras, communication devices, trains, ATMs, etc.