Question

A box contains 4 bad and 6 good tubes. two are drawn out from the box at a time. one of them is tested and found to be good. what is the probability that the other one is also good

Answer 1

Given,

In a box;

Number of good tubes = 6

Number of bad tubes = 4

To find,

The probability that the second tube picked up is good.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

The probability of occurrence of a favorable event = P (favorable event)

= (Total number of occurrence of the favorable event) / (Total number of occurrence of all possible events)

= (Total number of occurrence of the favorable event) / (Total number of trials)

Now, according to the question;

after the first good tube picked up,

number of good tubes left = 5

number of bad tubes left = 4

Now,

The probability that the second tube picked up is good

= (Total number of good tubes left) / (Total number of tubes remaining)

= 5/(10-1)

= 5/9

Hence, 5/9 is the probability that the second tube picked up is good.

Answer 2

5/13 is the probability that the other one is also good if  one of them is tested and found to be good

Given:

• A box contains 4 bad and 6 good tubes.
• Two are drawn out from the box at a time
• One of them is tested and found to be good

To Find:

• The probability that the other one is also good

Step 1:

Number of ways 2 Tubes out of 10 ( 4 bad + 6 good) can be selected is

¹⁰C₂ = 45

Step 2:

Number of ways at least one good tube is selected = Total ways - both bad selected

45 - ⁴C₂  = 39

Step 3:

Number of ways  both good selected

⁶C₂  = 15

Step 2:

Number of ways at least one good tube is selected = Total ways - both bad selected

45 - ⁴C₂  = 39

Step 4:

Probability of other being good if one is good is

15/39

= 5/13

Hence , 5/13 is the probability that the other one is also good if  one of them is tested and found to be good