Dependent and Independent Events

If you have events that occur together or in a row, they are considered to be compound events (involve two or more separate events) If the occurrence of one event has nothing to do with the other, the events are considered to be INDEPENDENT. Ex. What is the probability of drawing a red card from a full deck of card? What is the probability of drawing a red card again if the first card was placed back in the deck?

What is the probability of turning five red cards in a row? Example What is the probability of flipping a coin and rolling a three on a die? ½ x 1/6 according to our theory. Therefore we know that P(A and B) = P(A) x P(B) for events that are independent.

Example The probability that it is going to be sunny is 0.4 when walking to school. The probability of meeting up with your friend on the way to school is 0.3. a) What is the prob of it being sunny and walking to school with your friend? b) What is the prob of it not being sunny and walking to school with your friend? c) What are the odds of it being sunny and walking to school without your friend?

In some cases, something will have to happen first before something else can happen. For example, If the outcome of an event directly depends on the outcome of another event, they are said to be dependent. This becomes conditional probability. If the outcome of B is dependent of the outcome of A, then the cond. Prob. of B, P(B|A), is the probability that B occurs, given that A has already occurred.

Ex. In order to match up socks in a drawer, there are 4 black socks, 6 red socks and 2 blue socks. What is the probability that two black socks will be chosen out of the drawer? In this question there are 12 socks in total. We want to choose 1 black sock first out of a total of 4 black socks, therefore our probability of choosing a black sock is 4/12.

To choose the second black sock, we now have 11 socks to choose from and only 3 black chances, therefore our probability of choosing a black sock is 3/11. Our total probability is calculated to be 4/12 x 3/11 = 1/11 or 0.09 = 9% chance In that example, when two events are dependent we still multiply the probabilities together, however we must use the conditional prob for the second event. Product rule for dependent events. P(A and B) = P(A) x P(B|A)

Remember that we can use this as a formula. If we know the first and second items, we can easily get the third item in the equation! Homework Pg 334 # 1, 2,3,6,9,10, 17 try it