Question

Two balls are drawn at random, with replacement from a box containing 9 black and 7
white balls. Calculate the probability of both balls are black. ​

Answer 1

I ask this question from my brother (◕ᴗ◕✿)

Step-by-step explanation:

Probability of both ball are black is 81/256 = 0.32

Step-by-step explanation:

There are 9 black and 7 white balls. Thus, total number of balls is 16

Probability of an event E is given by

P(E)=\frac{n(E)}{n(S)}P(E)=

n(S)

n(E)

Here, n(s) = 16

In the first drawn, the probability of getting a black ball is given by

P(E_1)=\frac{9}{16}P(E

1

)=

16

9

Now, replacement is allowed, hence the total number of balls in second drawn is also 16

The probability of getting a black ball in second drawn is given by

P(E_2)=\frac{9}{16}P(E

2

)=

16

9

Therefore, probability for both black balls is

\begin{gathered}P(E)=P(E_1)\times P(E_2)\\\\P(E)=\frac{9}{16}\times \frac{9}{16}\\\\P(E)=\frac{81}{256}\approx 0.32\end{gathered}

P(E)=P(E

1

)×P(E

2

)

P(E)=

16

9

×

16

9

P(E)=

256

81

≈0.32