Probability HSC question (1 Viewer)

[BlueGas]

I need help with ii) and iii).

For ii), why isn't it 1/3 x 2/3 x 3/3?

 

[rand_althor]

For ii), why isn't it 1/3 x 2/3 x 3/3?

If James has to search all three levels before finding his car, then it has to be on the last level he searches. At first, there are three levels he can choose from to search. Two of the levels don't have his car, so there is a 2/3 chance that James will search a level that does not have his car. Once he has searched that level, there are two remaining levels, one of which has his car. There is a 1/2 chance that James will pick the wrong level to search. Finally, there is only level for James to search, and since this level has his car, the chance of him finding it there is 1.

For (iii), there is a 1/3 chance that James will pick the correct level straight away. We want the complementary event of this, which is James picking the incorrect level initially. This event has a 2/3 chance of happening. Since the question asks for the chance of this happening for 5 days we multiply the probabilities, calculating 2/3 * 2/3 * 2/3 * 2/3 * 2/3, or (2/3)^5.

 

[braintic]

Part (ii) doesn't need any calculation.
The probability that the car is on the last level he happens to choose is clearly one in three.

 

[calamebe]

Basically for ii) the question is without replacement, James isn't going to go back to a level he has already searched. For iii) it is just the probability that he will search the wrong floor first for 5 days in a week. As the chance he will choose the right floor is 1/3, the chance he will not is 2/3. So therefore the probability that he will search the wrong floor first every day of the working week is (2/3)^5.