Give your answer as a decimal correct to three significant figures.

Question

A bag of sweets contains 5 chocolates(C), 10 toffees(T) and 7 licorice(L). Amy takes a sweet from the bag and eats it, then selects a second one and eats that. What is the probability that she eats one toffee and one chocolate? Give your answer as a decimal correct to three significant figures.

Answer 1

I would solve this by making a probability tree. Stage 1 has three branches labeled T,C,L and the individual probabilities associated with these are 10/22, 5/22, 7/22, respectively.

 

From the end of each of these three limbs, construct 3 limbs for Stage 2, labeled CTL, respectively.

 

Choose the node associated with T (stage 1) and C (stage 2). The prob of C at stage 2 is 5/21 and so this TC path has probability (10/22)(5/21).

 

But there's one other way to satisfy the event, namely the path where C is stage 1, T is stage 2; this probability is (5/22)(10/21).

 

Each probability cited above (TC and CT) has value 25/(11•21) so the P(one choc, one toffee) is twice this value.

You can compute this in decimal, yourself.

 

Answer 2

(10/22)(5/21) = ?