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JEE Advanced 2008Paper 2
Exam
JEE Advanced
Year
2008
Paper
Paper 2
Subject
Mathematics
Chapter
Probability

JEE Advanced 2008 · Paper 2 · Mathematics · Probability

An experiment has 10 equally likely outcomes. Let A and B be two...

An experiment has 10 equally likely outcomes. Let AA and BB be two non-empty events of the experiment. If AA consists of 4 outcomes, the number of outcomes that BB must have so that AA and BB are independent, is

Options

  1. A2,4 or 8
  2. B3,6 or 9
  3. C4 or 8
  4. D5 or 10

Correct answer

D. 5 or 10

Step-by-step solution

P(A)=25P(A)=\frac{2}{5} For independent events, P(A∩B)=P(A)P(B)⇒P(A∩B)≤25⇒P(A∩B)=110,210,310,410 (i) P(A∩B)=110⇒P(A)\cdotP(B)=110⇒P(B)=110×52=14, not possible.  (ii) P(A∩B)=210⇒25\timesP(B)=210⇒P(B)=510, outcomes of B=5\begin{aligned}& P(A \cap B)=P(A) P(B) \Rightarrow P(A \cap B) \leq \frac{2}{5}\\ & \Rightarrow P(A \cap B)=\frac{1}{10}, \frac{2}{10}, \frac{3}{10}, \frac{4}{10}\\ & \text{ (i) }P(A \cap B)=\frac{1}{10}\\ & \Rightarrow P(A) \cdotP(B)=\frac{1}{10}\\ & \Rightarrow \quad P(B)=\frac{1}{10} \times \frac{5}{2}=\frac{1}{4}, \text{ not possible. }\\ & \text{ (ii) }P(A \cap B)=\frac{2}{10} \Rightarrow \frac{2}{5} \timesP(B)=\frac{2}{10}\\ & \Rightarrow \quad P(B)=\frac{5}{10}, \text{ outcomes of }B=5 \end{aligned}\text{ (iii) } P(A∩B)=310\RightarrowP(A)\cdotP(B)=310⇒25\timesP(B)=310P(B)=34, not possible \begin{aligned}& P(A \cap B)=\frac{3}{10} \RightarrowP(A) \cdotP(B)=\frac{3}{10}\\ & \Rightarrow \quad \frac{2}{5} \timesP(B)=\frac{3}{10}\\ & P(B)=\frac{3}{4}, \text{ not possible } \end{aligned} \text{ (iv) } P(A∩B)=410⇒P(A)\cdotP(B)=410⇒P(B)=1, outcomes of B=10.\begin{aligned}& P(A \cap B)=\frac{4}{10}\\ \Rightarrow & P(A) \cdotP(B)=\frac{4}{10}\\ \Rightarrow & P(B)=1, \text{ outcomes of }B=10 . \end{aligned}
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