PROBABILITY PART II

On our previous lesson, we learnt about single events in probability. But today, we will be moving to the next stage which is multiple events.
Multiple Events

Independent and Dependent Events
If incase now we consider the probability of 2 events happening. For instance, we might throw 2 dice and consider the probability that both are 6's.

We define two events independent if the outcome of one of the events does no effect on the outcome of another. For instance, if you throw two dice, the probability of getting a 6 on the second die is the same, no matter what we get from the first one- it's still 1/6.

On the other hand, suppose we have a box containing 2 green and 2 blue balls. If we pick 2 balls out of the box, the probability that the second is blue depends upon what the colour of the first ball picked was. If the first ball was blue, there will be 1 blue and 2 red balls in the box when we pick the second ball. So the probability of getting a blue is 1/3. However, if the first ball was red, there will be 1 red and 2 blue balls left so the probability the second ball is blue is 2/3. When the probability of one event depends on another, the events are dependent.

WAYS OF FINDING THE PROBABILITY OF MULTIPLE EVENTS

Possibility Spaces:
When working out what the probability of two things happening is, the possibility space can be drawn. For instance, if you throw two dice, what is the probability that you will get: a) 8, b) 9, c) either 8 or 9?

a) The black blobs indicate the ways of getting 8 (a 2 and a 6, a 3 and a 5, ...). There are 5 different ways. The probability space shows us that when throwing 2 dice, there are 36 different possibilities (36 squares). With 5 of these possibilities, you will get 8. Therefore P(8) = 5/36 .
b) The red blobs indicate the ways of getting 9. There are four ways, therefore P(9) = 4/36 = 1/9.
c) You will get an 8 or 9 in any of the 'blobbed' squares. There are 9 altogether, so P(8 or 9) = 9/36 = 1/4 .

END OF LESSON EXERCISE

1. Sample problem: Eight five % of employees have health insurance. Out of those 85%, 45% had deductibles higher than $1,000. What percentage of people had deductibles higher than $1,000?”

2. Sample problem: The odds of you getting a job you applied for are 45% and the odds of you getting the apartment you applied for are 75%. What is the probability of you getting both the new job and the new car?