Question

A man draws at random 3 balls from a bag containing 6 red and 5 white balls. What is the chance of getting the balls all red.

Answer 1

3 is the answer

because 6 red balls are there in a bag we are taking 3balls so the chance will be3/6

Answer 2

The chance of getting the balls all red = 4/33

Given :

A man draws at random 3 balls from a bag containing 6 red and 5 white balls

To find :

The chance of getting the balls all red

Solution :

Step 1 of 2 :

Find total number of possible outcomes

Total number of balls in the bag

= 6 + 5

= 11

Now 3 balls are drawn from the bag

Total number of possible outcomes

$\displaystyle \sf{ = {}^{11} C_3 }$

$\sf = 165$

Step 2 of 3 :

Find total number of possible outcomes for the event

Let A be the event that of getting the balls all red

Since there are 6 red balls in the bag

So total number of possible outcomes for the event A

$\displaystyle \sf{ = {}^{6} C_3 }$

$\displaystyle \sf{ = 20 }$

Step 3 of 3 :

Find chance of getting the balls all red

The chance of getting the balls all red

= P(A)

$\displaystyle \sf{ = \frac{Number \: of \: favourable \: cases \: to \: the \: event \: A }{Total \: number \: of \: possible \: outcomes }}$

$\displaystyle \sf{ = \frac{20}{165} }$

$\displaystyle \sf{ = \frac{4}{33} }$