SATHEE: Probability 3 Question 8

Probability 3 Question 8

8. Four persons independently solve a certain problem correctly with probabilities $\frac{1}{2}, \frac{3}{4}, \frac{1}{4}, \frac{1}{8}$ . Then, the probability that the problem is solved correctly by atleast one of them, is

(a) $\frac{235}{256}$

(b) $\frac{21}{256}$

(d) $\frac{253}{256}$

(2013 Adv)

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Solution:

PLAN It is simple application of independent event, to solve a certain problem or any type of compitition each event in independent of other.

Formula used

$P (A \cap B) = P (A) \cdot P (B)$ , when $A$ and $B$ are independent events.

Probability that the problem is solved correctly by atleast one of them $= 1 -$ (problem is not solved by all)

$∴ P ($ problem is solved $) = 1 - P ($ problem is not solved $)$

$\begin{aligned} = 1 - P (\bar{A}) \cdot P (\bar{B}) \cdot P (\bar{C}) \cdot P (\bar{D}) \\ = 1 - \frac{1}{2} \cdot \frac{1}{4} \cdot \frac{3}{4} \cdot \frac{7}{8} = 1 - \frac{21}{256} = \frac{235}{256} \end{aligned}$

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Probability 3 Question 8

8. Four persons independently solve a certain problem correctly with probabilities $\frac{1}{2}, \frac{3}{4}, \frac{1}{4}, \frac{1}{8}$ . Then, the probability that the problem is solved correctly by atleast one of them, is

Solution:

Formula used

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 8

8. Four persons independently solve a certain problem correctly with probabilities 12,34,14,18. Then, the probability that the problem is solved correctly by atleast one of them, is

Solution:

Formula used

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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8. Four persons independently solve a certain problem correctly with probabilities $\frac{1}{2}, \frac{3}{4}, \frac{1}{4}, \frac{1}{8}$ . Then, the probability that the problem is solved correctly by atleast one of them, is