SATHEE: Probability 4 Question 6

Probability 4 Question 6

6. Let $H_{1}, H_{2}, \dots, H_{n}$ be mutually exclusive events with $P (H_{i}) > 0, i = 1, 2, \dots, n$ . Let $E$ be any other event with $0 < P (E) < 1$ .

Statement I $P (H_{i} / E) > P (E / H_{i}) \cdot P (H_{i})$ for $i = 1, 2, \dots, n$ Statement II $\sum_{i = 1}^{n} P (H_{i}) = 1$

(2007, 3M)

Passage Based Problems

Passage I

Let $n_{1}$ and $n_{2}$ be the number of red and black balls, respectively in box I. Let $n_{3}$ and $n_{4}$ be the number of red and black balls, respectively in box II.

(2015 Adv.)

Show Answer

Answer:

Correct Answer: 6. (d)

Solution:

Statement I If $P (H_{i} \cap E) = 0$ for some $i$ , then

$P \frac{H_{i}}{E} = P \frac{E}{H_{i}} = 0$

If $P (H_{i} \cap E) \neq 0, \forall i = 1, 2, \dots, n$ , then

$\begin{aligned} P \frac{H_{i}}{E} = \frac{P (H_{i} \cap E)}{P (H_{i})} \times \frac{P (H_{i})}{P (E)} \\ = \frac{P \frac{E}{H_{i}} \times P (H_{i})}{P (E)} > P \frac{E}{H_{i}} \cdot P (H_{i}) [∵ 0 < P (E) < 1] \end{aligned}$

Hence, Statement I may not always be true.

Statement II Clearly, $H_{1} \cup H_{2} \cup \dots \cup H_{n} = S$

[sample space]

$\Rightarrow P (H_{1}) + P (H_{2}) + \dots + P (H_{n}) = 1$

Hence, Statement II is ture.

Passage I

पिछला

अगला

Probability 4 Question 6

6. Let $H_{1}, H_{2}, \dots, H_{n}$ be mutually exclusive events with $P (H_{i}) > 0, i = 1, 2, \dots, n$ . Let $E$ be any other event with $0 < P (E) < 1$ .

Passage Based Problems

Passage I

Answer:

Passage I

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Probability 4 Question 6

6. Let H1,H2,…,Hn be mutually exclusive events with P(Hi)>0,i=1,2,…,n. Let E be any other event with 0<P(E)<1.

Passage Based Problems

Passage I

Answer:

Passage I

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Menu

6. Let $H_{1}, H_{2}, \dots, H_{n}$ be mutually exclusive events with $P (H_{i}) > 0, i = 1, 2, \dots, n$ . Let $E$ be any other event with $0 < P (E) < 1$ .