Question

Steve has 10 biscuits in a tin. There are 3 digestive, 2 chocolate and 5 ginger biscuits. Steve takes two biscuits at random from the tin. Work out the probability that he chooses two different types of biscuits.

Answer 1

Explanation:

There are 10*9 ways of selecting two biscuits (in order 1,2)

Of these 90 possible orders

2 digestives can be picked in 5*4 ways =20

2 chocolate can be picked in 2*1 ways = 2

2 ginger can be picked in 3*2 ways =6

Digestive then chocolate can be selected 5*2 ways =10

Chocolate then Digestive can be selected 2*5 ways = 10

Digestive then ginger can be selected 5*3 ways ways = 15

Ginger then digestive can be selected 3*5 ways ways = 15

Chocolate then Ginger can be selected 2*3 ways =6

Ginger then chocolate can be selected 3*2 ways = 6

I have done this the ‘long’ way to demonstrate that all 90 possible outcomes are covered. (Double check)

Probability of taking two different is then the total of the last 6 options divided by the total number of options = 2*(10+15+6)/90 = 31/45 = 68.89% (Approx.)

Answer 2

0%

Explanation: