Question

From qn urn containing 4 white and 5 red balls,two balls are drawn at random .find the probability that at least one is white​

Answer 1

4+5=9

so probability of getting white ball will be

4/9....

Answer 2

Answer:

13 / 18

( It is mentioned in discussion below that the answer should be 18/21... That is not correct for the problem as stated. )

Step-by-step explanation:

To help make things clear, let's look at this in two different ways.

Method 1

P(at least one white ball)

= 1 - P(two red balls)

= 1 - ( # ways choosing 2 red balls ) / ( # ways choosing 2 balls )

= $\displaystyle 1 - \frac{\binom52}{\binom92}$

= 1 - 10/36

= 1 - 5/18

= 13 / 18

Method 2

Since the numbers are small, we can actually list all possibilities.  This makes it clear and safe since there's no reasoning around what the appropriate calculation would be.

Mark the balls with the numbers 1 to 9, so that balls 1 to 4 are white and 5 to 9 are red.

Then the possible ways for drawing two balls are:

12 13 14 15 16 17 18 19 23 24 25 26 27 28 29 34 35 36 37 38 39 45 46 47 48 49 56 57 58 59 67 68 69 78 79 89

Counting them, there are 36 possible outcomes.

The outcomes that match the condition "at least one is white" have been marked in bold italics.  Counting them, there are 26 outcomes.

So...

P(at least one white ball) = 26 / 36 = 13 / 18