Propability female and extra treatment I have the following scenario: > It has been found that 55% of patients arriving at the A&E department are male. Furthermore, 10% of all arrivals are required to return for extra treatment. With the following questions: a) both are male; 0.55 * 0.55 = 30% b) both require additional treatment; 0.1 * 0.1 = 1% c) only one patient requires additional treatment; 0.1 * 0.9 = 9% d) the first patient requires treatment and the second patient is female; 0.1 * 0.45 = 4,5% e) only one patient is female. 0,45 * 0,55 = 24,75% **Are my results correct?** Thanks

For both parts (c) and (e), your answers are half of what they should be. In the case of (c), you have calculated the probability that the first patient requires extra treatment and the second one does not. You should also consider the possibility that the first does not, but the second does. Thus, you will have:

$$0.1\cdot 0.9 + 0.9\cdot 0.1$$

or simply:

$$2\cdot 0.1\cdot 0.9$$

Similar considerations apply to part (e).