AP EAMCET · Maths · Probability

A bag \(P\) contains 5 white marbles and 3 black marbles. Four marbles are drawn at random from \(P\) and are put in an empty bag \(Q\). If a marble drawn at random from \(Q\) is found to be black then the probability that all the three black marbles in \(P\) are transfered to the bag \(Q\) is.

A \(\frac{1}{7}\)
B \(\frac{6}{7}\)
C \(\frac{1}{8}\)
D \(\frac{7}{8}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{1}{7}\)

Step-by-step Solution

Detailed explanation

Here, \(W=\) White, \(B=\) Black. Given that bag \(P\) contains \(5 W\) marbles and \(3 B\) marbles. 4 marbles are drawn from the bag \(P\) and \(A\) black marble is drawn from bag \(Q\). Let Event \(E_1: 1 \mathrm{~W}\) and \(3 \mathrm{~B}\) marbles are transferred Event…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Match the ranges of the functions given in List - I with those of the items given in List - II

List - I	List - II
(I) \(3 \sin ^2 x+4 \cos ^2 x-2\)	(a) \(\left[\frac{1}{4}, 1\right]\)
(II) \(\cos ^2 x+\sin ^4 x\)	(b) \(\left[-\frac{1}{4}, \frac{1}{4}\right]\)
(III) \(\sin ^6 x+\cos ^6 x\)	(c) \([1,2]\)
(IV) \(\cos x \cos \left(\frac{2 \pi}{3}+x\right) \cos \left(\frac{2 \pi}{3}-x\right)\)	(d) \(\left[\frac{3}{4}, 1\right]\)
	(e) \([0,1]\)

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