An urn contains 5 red... | Probability

JEE MAIN 2019

09-01-19 S2

Question

An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is

Select the correct option:

$\frac{26}{49}$

$\frac{21}{49}$

$\frac{32}{49}$

$\frac{27}{49}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Let drawing a green ball is G and a red ball is R ∴ The probability that second drawn ball is red $$ \begin{aligned} & =P(G) \cdot P\left(\frac{R}{G}\right)+P(R) P\left(\frac{R}{R}\right) \\ & =\frac{2}{7} \times \frac{6}{7}+\frac{5}{7} \times \frac{4}{7} \\ & =\frac{12+20}{49} \\ & =\frac{32}{49} \end{aligned} $$

Question Tags

JEE Main

Mathematics

Easy

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