
An urn contains 3 red and 5 blue balls. The probability that two balls are drawn in which 2nd ball drawn is blue without replacement is:
A. $\dfrac{5}{{16}}$
B. $\dfrac{5}{{56}}$
C. $\dfrac{5}{8}$
D. $\dfrac{{20}}{{56}}$
Answer
164.1k+ views
Hint: There are two cases to solve the equations. First case: the first ball is in red color and the second ball is blue in color. Second case: the first ball is blue in color and the second ball is blue in color. Then add the probability of two cases to get the required solution.
Formula Used:
Required Probability $ = P$ (First ball is red, second ball is blue) $ + P$ (First ball is blue, second ball is blue)
Complete step by step solution:
We have been given that total number of balls $ = 3 + 5 = 8{\rm{ balls}}$
Probability of first ball is red & second ball is blue $ = \dfrac{3}{8} \cdot \dfrac{5}{7}$
Probability of first ball is blue & second ball is blue $ = \dfrac{5}{8} \cdot \dfrac{4}{7}$
Therefore,
Required Probability $ = P$ (First ball is red, second ball is blue) $ + P$ (First ball is blue, second ball is blue)
Required Probability $ = \dfrac{3}{8} \cdot \dfrac{5}{7} + \dfrac{5}{8} \cdot \dfrac{4}{7}$
Hence, the probability that the second ball drawn is red $ = \dfrac{5}{8}$.
Option ‘C’ is correct
Note: We have to use the concept of probability distribution to solve the question which states that probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about how probable an event is to happen, or its likelihood of happening. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty.
Formula Used:
Required Probability $ = P$ (First ball is red, second ball is blue) $ + P$ (First ball is blue, second ball is blue)
Complete step by step solution:
We have been given that total number of balls $ = 3 + 5 = 8{\rm{ balls}}$
Probability of first ball is red & second ball is blue $ = \dfrac{3}{8} \cdot \dfrac{5}{7}$
Probability of first ball is blue & second ball is blue $ = \dfrac{5}{8} \cdot \dfrac{4}{7}$
Therefore,
Required Probability $ = P$ (First ball is red, second ball is blue) $ + P$ (First ball is blue, second ball is blue)
Required Probability $ = \dfrac{3}{8} \cdot \dfrac{5}{7} + \dfrac{5}{8} \cdot \dfrac{4}{7}$
Hence, the probability that the second ball drawn is red $ = \dfrac{5}{8}$.
Option ‘C’ is correct
Note: We have to use the concept of probability distribution to solve the question which states that probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about how probable an event is to happen, or its likelihood of happening. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty.
Recently Updated Pages
Geometry of Complex Numbers – Topics, Reception, Audience and Related Readings

JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

Atomic Structure - Electrons, Protons, Neutrons and Atomic Models

Displacement-Time Graph and Velocity-Time Graph for JEE

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Learn About Angle Of Deviation In Prism: JEE Main Physics 2025

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

NCERT Solutions for Class 11 Maths Chapter 4 Complex Numbers and Quadratic Equations

JEE Advanced Weightage 2025 Chapter-Wise for Physics, Maths and Chemistry

Degree of Dissociation and Its Formula With Solved Example for JEE

Instantaneous Velocity - Formula based Examples for JEE

NCERT Solutions for Class 11 Maths In Hindi Chapter 1 Sets
