SATHEE: Probability 3 Question 2

Probability 3 Question 2

2. Four persons can hit a target correctly with probabilities $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}$ and $\frac{1}{8}$ respectively. If all hit at the target independently, then the probability that the target would be hit, is

(2019 Main, 9 April I)

(a) $\frac{1}{192}$

(b) $\frac{25}{32}$

(d) $\frac{25}{192}$

Show Answer

Answer:

Correct Answer: 2. (b)

1. (d)	2. (b)	3. (b)	4. (a)
5. (c)	6. (d)	7. (a)	8. (a)
9. (d)	10. (c)	11. (c)	12. (b)
13. (b)	14. (a)	15. (a)	16. (b)
17. (a)	18. (c)	19. (b)	20. (b)
21. (a, b)	22. (a,b)	23. (a, d)	24. (b, c)
25. (a, d)	26. (a, d)	27. (a, c)	28. (b, c, d)
29. $\frac{1}{4}$	30. $\frac{5}{7}$	31. $\frac{2}{5}$	32. $\frac{32}{55}$
33. $\frac{1}{9}$	35. $\frac{1}{2}$	36. $2 p^{2} - p^{3}$	38. $\frac{193}{792}$

Solution:

Key Idea Use $P (\bar{A}) = 1 - P (A)$ and condition of independent events i.e $P (A \cap B) = P (A) \cdot P (B)$

Given that probability of hitting a target independently by four persons are respectively

$P_{1} = \frac{1}{2}, P_{2} = \frac{1}{3}, P_{3} = \frac{1}{4} and P_{4} = \frac{1}{8}$

Then, the probability of not hitting the target is

$= 1 - \frac{1}{2} 1 - \frac{1}{3} 1 - \frac{1}{4} 1 - \frac{1}{8}$

$= \frac{1}{2} \times \frac{2}{3} \times \frac{3}{4} \times \frac{7}{8} = \frac{7}{32}$

$[∵$ events are independent]

Therefore, the required probability of hitting the target $= 1 - ($ Probability of not hitting the target)

$= 1 - \frac{7}{32} = \frac{25}{32}$

पिछला

अगला

Probability 3 Question 2

2. Four persons can hit a target correctly with probabilities $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}$ and $\frac{1}{8}$ respectively. If all hit at the target independently, then the probability that the target would be hit, is

Answer:

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 3 Question 2

2. Four persons can hit a target correctly with probabilities 12,13,14 and 18 respectively. If all hit at the target independently, then the probability that the target would be hit, is

Answer:

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

2. Four persons can hit a target correctly with probabilities $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}$ and $\frac{1}{8}$ respectively. If all hit at the target independently, then the probability that the target would be hit, is