Answer
Verified
425.4k+ views
Hint: Probability is the ratio of number of favorable outcomes to the number of total outcomes, use this property to reach the answer.
The urn contains 5 red and 5 black balls.
Therefore total ball becomes $ = 5 + 5 = 10$
Let a red ball be drawn in the first attempt.
$\therefore {P_1} $(Drawing a red ball) $ = \dfrac{{{\text{Red balls}}}}{{{\text{Total balls}}}}$$ = \dfrac{5}{{10}} = \dfrac{1}{2}$
If two red balls are added to the urn, then the urn contains 7 red and 5 black balls.
So, red ball becomes $ = 7$
Therefore total ball becomes $ = 7 + 5 = 12$
$\therefore {P_2} $ (Drawing a red ball) $ = \dfrac{{{\text{Red balls}}}}{{{\text{Total balls}}}}$$ = \dfrac{7}{{12}}$
Again, the urn contains 5 red and 5 black balls.
Therefore total ball becomes $ = 5 + 5 = 10$
Now let a black ball be drawn in the first attempt.
$\therefore {P_3}$ (Drawing a black ball) $ = \dfrac{{{\text{Black balls}}}}{{{\text{Total balls}}}}$$ = \dfrac{5}{{10}} = \dfrac{1}{2}$
If two black balls are added to the urn, then the urn contains 5 red and 7 black balls.
Therefore total ball becomes $ = 5 + 7 = 12$
$\therefore {P_4}$ (Drawing a red ball) $ = \dfrac{{{\text{Red balls}}}}{{{\text{Total balls}}}}$$ = \dfrac{5}{{12}}$
Therefore, probability of drawing second ball as red is
${P_r} = \left( {{P_1} \times {P_2}} \right) + \left( {{P_3} \times {P_4}} \right)$ (conditional probability)
${P_r} = \dfrac{1}{2} \times \dfrac{7}{{12}} + \dfrac{1}{2} \times \dfrac{5}{{12}} = \dfrac{1}{2} \times \left( {\dfrac{7}{{12}} + \dfrac{5}{{12}}} \right) = \dfrac{1}{2} \times \dfrac{{12}}{{12}} = \dfrac{1}{2}$
So the required probability is $\dfrac{1}{2}$
Note: In such types of questions the key concept we have to remember is that always remember the formula of probability which is stated above, then according to given conditions calculate different probabilities and then finally calculate your required probability using the formula which is stated above, we will get the desired answer.
The urn contains 5 red and 5 black balls.
Therefore total ball becomes $ = 5 + 5 = 10$
Let a red ball be drawn in the first attempt.
$\therefore {P_1} $(Drawing a red ball) $ = \dfrac{{{\text{Red balls}}}}{{{\text{Total balls}}}}$$ = \dfrac{5}{{10}} = \dfrac{1}{2}$
If two red balls are added to the urn, then the urn contains 7 red and 5 black balls.
So, red ball becomes $ = 7$
Therefore total ball becomes $ = 7 + 5 = 12$
$\therefore {P_2} $ (Drawing a red ball) $ = \dfrac{{{\text{Red balls}}}}{{{\text{Total balls}}}}$$ = \dfrac{7}{{12}}$
Again, the urn contains 5 red and 5 black balls.
Therefore total ball becomes $ = 5 + 5 = 10$
Now let a black ball be drawn in the first attempt.
$\therefore {P_3}$ (Drawing a black ball) $ = \dfrac{{{\text{Black balls}}}}{{{\text{Total balls}}}}$$ = \dfrac{5}{{10}} = \dfrac{1}{2}$
If two black balls are added to the urn, then the urn contains 5 red and 7 black balls.
Therefore total ball becomes $ = 5 + 7 = 12$
$\therefore {P_4}$ (Drawing a red ball) $ = \dfrac{{{\text{Red balls}}}}{{{\text{Total balls}}}}$$ = \dfrac{5}{{12}}$
Therefore, probability of drawing second ball as red is
${P_r} = \left( {{P_1} \times {P_2}} \right) + \left( {{P_3} \times {P_4}} \right)$ (conditional probability)
${P_r} = \dfrac{1}{2} \times \dfrac{7}{{12}} + \dfrac{1}{2} \times \dfrac{5}{{12}} = \dfrac{1}{2} \times \left( {\dfrac{7}{{12}} + \dfrac{5}{{12}}} \right) = \dfrac{1}{2} \times \dfrac{{12}}{{12}} = \dfrac{1}{2}$
So the required probability is $\dfrac{1}{2}$
Note: In such types of questions the key concept we have to remember is that always remember the formula of probability which is stated above, then according to given conditions calculate different probabilities and then finally calculate your required probability using the formula which is stated above, we will get the desired answer.
Recently Updated Pages
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
What are the possible quantum number for the last outermost class 11 chemistry CBSE
Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
What is BLO What is the full form of BLO class 8 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The cell wall of prokaryotes are made up of a Cellulose class 9 biology CBSE
What organs are located on the left side of your body class 11 biology CBSE
Select the word that is correctly spelled a Twelveth class 10 english CBSE
a Tabulate the differences in the characteristics of class 12 chemistry CBSE