Question

A box contains 5 black and 3 green shirts.One shirt is picked randomly and put into other box.

Answer 1

Answer:

1/2 chance in any one box it should be green or it should be black

Answer 2

Q) A box has 5black and 3green shirts. One shirt is picked randomly and put in another box. The second box has 3black and 5green shirts. Now a shirt is picked from the second box. What is the probability of being a black shirt?

a)   $\frac{4}{9}$ .

b)   $\frac{29}{72}$.

c)    $\frac{8}{72}$.

d)    $\frac{3}{16}$.

Option (b) 29/72 is the correct answer.

Given,

In box 1, 5black and 3green shirts.

In box 2, 3black and 5green shirts.

To Find,

The probability of being the picked one is a black shirt.

Solution,

Given that,

there are two boxes.

And in the first box, it contains 5balck and 3green shirts.

And one shirt is randomly selected and picked from the first box.

So there will be two cases,

i) The picked shirt from the box is black.

ii) Green is the shirt picked.

In the first case,

If the picked shirt is black.

Box 1 has a total of 8 shirts( 5+3).

The number of black shirts = 5.

So, the probability of a black shirt from the first box = $\frac{5}{8}$.

And, that black shirt is put into the second box.

Then the total number of shirts in the box 2 will be

1  + 3 + 5 =9

And the black shirt will be = 4

So, the black from box 2 probability = $\frac{4}{9}$

In the first case the probability of a black shirt

$\frac{5}{8} * \frac{4}{9}$  = 20 / 72.

In case 2, the shirt picked from box 2 is green.

The Number of the green shirt in box 1 = 3.

Green shirt's probability = $\frac{3}{8}$

When that green shirt is added to the second box, the number of green shirts will be 6.

And in box 2 total 9shirts.

In that case the black shirt probability from the box 2 = $\frac{3}{9}$.

The probability of case 2 = $\frac{3}{8}* \frac{3}{9}$

9/72.

Then the overall probability = $\frac{20}{72} + \frac{9}{72}$

$\frac{29}{72}$

Hence, $\frac{29}{72}$  is the probability of the picked shirt is being a black shirt.

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