successive outcomes

Question

A bag contains 5 red,3blue and 2 yellow counters. One counter is drawn at random, then it is replaced after its colour has been noted and another drawn. What is the probability that both counters are blue

Answer 1

The probability that a first counter drawn is blue is 3/10 or P(B₁)=0.3. There are 3 blues out of 10 counters.

Since the counter is replaced, the probability of the second counter being blue is also 3/10 or P(B₂)= 0.3.

These events are independent (the outcome of the first draw doesn't effect the outcome of the second draw. We know this because the counter is replaced after each draw).

Since they are independent you can multiply each probability: P(B₁B₂) = 0.3*0.3 = 0.09.