Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Provide solution for RD Sharma Maths Class12 Chapter 30 Probability Exercise Fill in the Blanks Question, Question 2.

Provide solution for RD Sharma Maths Class12 Chapter 30 Probability Exercise Fill in the Blanks Question, Question 2.

Answers (1)

Answer:   \frac{5}{12},\frac{1}{3}

Given:

If A and B are independent events such-that

PA=p,

P(B)=2pand

P( Exactly one ofA_1B=\frac{5}{9}) then

p=?

Hint:

P(A \cap A B)=P(A) P(B) if A and B are independent.

Explanation:

As A and B ane independent events.
So P(A \cap A B)=P(A) P(B)       - (1)

Now
P( Exadly one of A and B occurs )= \frac{5}{9}
⇒P( only A)+P( onlyB)= \frac{5}{9}

\begin{aligned} &\Rightarrow[\mathrm{P}(\mathrm{A})-\mathrm{P}(\mathrm{A} \cap \mathrm{B})]+[\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A} \cap \mathrm{B})]=\frac{5}{9} \\ &\Rightarrow[\mathrm{P}(\mathrm{A})-\mathrm{P}(\mathrm{A}) \mathrm{P}(\mathrm{B})]+[\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A}) \mathrm{P}(\mathrm{B}))]=\frac{5}{9} \\ &\Rightarrow\left[\mathrm{P}(\mathrm{A}) \times(1-\mathrm{P}(\mathrm{B}))+\mathrm{P}(\mathrm{B}) \times[1-\mathrm{P}(\mathrm{A})]=\frac{5}{9}\right. \\ &\Rightarrow \mathrm{p}(1-2 \mathrm{p})+2 \mathrm{p}(1-\mathrm{p})=\frac{5}{9} \\ &\Rightarrow \mathrm{p}-2 \mathrm{p}^{2}+2 \mathrm{p}-2 \mathrm{p}^{2}=\frac{5}{9} \\ &\Rightarrow 3 \mathrm{p}-4 \mathrm{p}^{2}=\frac{5}{9} \\ &\Rightarrow 27 \mathrm{p}-36 \mathrm{p}^{2}=5 \\ &\Rightarrow 36 \mathrm{p}^{2}-27 \mathrm{p}+5=0 \end{aligned}

So using quadratic formula, \mu.

\begin{aligned} &p=\frac{-(-27) \pm \sqrt{(-27)^{2}-4 \times 36 \times 5}}{2 \times 36} \\ &=\frac{27 \pm \sqrt{729-720}}{72} \\ &=\frac{27 \pm \sqrt{9}}{72} \\ &=\frac{27 \pm 3}{72} \end{aligned}

\begin{aligned} p &=\frac{27+3}{72}, \frac{27-3}{72} \\ &=\frac{30}{72}, \frac{24}{72} \\ &=\frac{5}{12}, \text { or } \frac{1}{3} \end{aligned}

Posted by

infoexpert24

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Board exams twice a year from 2025, no plan for semesters: MoE
anam-khan

CBSE Class 12 board exams 2025 to have 50% competency-based questions; no change in 10th
anam-khan

CBSE Class 12 board exams 2024 over; expected result date, trends of last 10 years

Latest Question