Steve has 8 biscuits in a tin. There are 3 digestive and 5 chocolate biscuits. Steve takes two biscuits at random from the tin. Work out the probability that he chooses two different types of biscuits.
Answers
Answer:
Steve has 12 biscuits in a tin. There are 7 digestive and 5 chocolate biscuits. Steve takes two biscuits at random from the tin. Work out the probability that he chooses two different types of biscuits?
There are C(12,2) = 66 ways to select 2 biscuits from a can of 12 (7 digestive, 5 chocolate)) biscuits, where C(12,2) = the combination of 12 items taken 2 at a time.
There are C(7,1)*C(5,1) = 35 ways to select 1 digestive biscuit out of 7 while at the same time selecting 1 chocolate biscuit out of 5.
Hence, the probability of selecting two different types of biscuits (a digestive and a chocolate) is 35/66 = 0.530 or 53%.
OR
Another way to approach this is as follows:
There are two ways to select the two different type of biscuits. You can select the digestive biscuit first (without replacing it) and then the chocolate biscuit or you can select the chocolate biscuit first (without replacing it) and then the digestive biscuit.
Hence the probability of selecting two different biscuits =
P(selecting digestive) * P(selecting chocolate I digestive selected first) +
P(selecting chocolate) * P(selecting digestive | chocolate selected first)
= 7/12 * 5/11 + 5/12 * 7/11 = 0.265152 + 0.265152 = 0.530
Hence, the probability of selecting two different types of biscuits is 0.530 or 53%