Question

You have a pot with 100 balls. 20 of them are red, 50 are blue and 30 are green. You decide to draw 5 balls from the pot without replacement (i.e. you don't put a ball back in the pot once it has been taken out). What is the probability of drawing five blue balls?

Give your answer to 3 decimal places.

Answer 1

A) Given data

Total balls=100

Red balls=20

Blue balls=50

Green balls=30

Sample space is =Drawing 5 balls from the pot without replacement

=100_{​​​​C}5

=100!/((100-5)!×(5!)

=100×99×98×97×96×95!/(95!×5!)

=100×99×98×97×96/(5!)

=(9034502400)/120

=75287520

Event is=drawing of 5 blue balls out of 50 blue balls

=50_C5

=50!/((50-5)!×(5!)

=50×49×48×47×46×45!/(45!×5!)

=50×49×48×47×46/(5!)

=(254251200)/(120)

=2118760

Now , required probability=Event/sample space

=2118760/(75287520)

=0.0281