SATHEE: Probability 5 Question 7

Probability 5 Question 7

7. Two cards are drawn successively with replacement from a well shuffled deck of 52 cards. Let $X$ denote the random variable of number of aces obtained in the two drawn cards. Then, $P (X = 1) + P (X = 2)$ equals

(a) $\frac{25}{169}$

(b) $\frac{52}{169}$

(d) $\frac{24}{169}$

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Answer:

Correct Answer: 7. (a)

Solution:

Let $p =$ probability of getting an ace in a draw $=$ probability of success

and $q =$ probability of not getting an ace in a draw $=$ probability of failure

Then, $p = \frac{4}{52} = \frac{1}{13}$

and $q = 1 - p = 1 - \frac{1}{13} = \frac{12}{13}$

Here, number of trials, $n = 2$

Clearly, $X$ follows binomial distribution with parameter $n = 2$ and $p = \frac{1}{13}$ .

Now, $P (X = x) =^{2} C_{x} {\frac{1}{13}}^{x} \frac{12}{13}^{2 - x}, x = 0, 1, 2$

$∴ P (X = 1) + P (X = 2)$

$=^{2} C_{1} {\frac{1}{13}}^{1} \frac{12}{13} +^{2} C_{2} {\frac{1}{13}}^{2} {\frac{12}{13}}^{0}$

$= 2 \frac{12}{169} + \frac{1}{169}$

$= \frac{24}{169} + \frac{1}{169} = \frac{25}{169}$

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Probability 5 Question 7

7. Two cards are drawn successively with replacement from a well shuffled deck of 52 cards. Let $X$ denote the random variable of number of aces obtained in the two drawn cards. Then, $P (X = 1) + P (X = 2)$ equals

Answer:

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Probability 5 Question 7

7. Two cards are drawn successively with replacement from a well shuffled deck of 52 cards. Let X denote the random variable of number of aces obtained in the two drawn cards. Then, P(X=1)+P(X=2) equals

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

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7. Two cards are drawn successively with replacement from a well shuffled deck of 52 cards. Let $X$ denote the random variable of number of aces obtained in the two drawn cards. Then, $P (X = 1) + P (X = 2)$ equals