Group1- Arti Chandavarkar

There are three types of events in Probability:

1. Mutually Exclusive

2. Independent

3. Dependent

1. Mutually Exclusive: Events that are different from each other are called mutually exclusive events. They cannot occur simultaneously. Examples:

• Turning left and turning right are Mutually Exclusive (not possible at the same time)
• Tossing a coin: Heads and Tails are Mutually Exclusive
• Cards: Kings and Aces are Mutually Exclusive

What is not Mutually Exclusive:

• Turning left and scratching your head can happen at the same time
• Kings and Hearts, because you can have a King of Hearts!

                                                  
Aces and Kings are                                                                 Hearts and Kings are Mutually exclusive Mutually Exclusive
 (can't be both) 

2. Independent Events: Two events are independent (alternatively called statistically independent or stochastically independent ) means that the occurrence of one does not affect the probability of the other. Similarly, two random variables are independent if the realization of one does not affect the probability distribution of the other.

Examples:

• Rolling a die- The event of getting a 6 the first time a die is rolled and the event of getting a 6 the second time are independent. By contrast, the event of getting a 6 the first time a die is rolled and the event that the sum of the numbers seen on the first and second trials is 8 are not independent.
• Drawing cards- If two cards are drawn with replacement from a deck of cards, the event of drawing a red card on the first trial and that of drawing a red card on the second trial are independent. By contrast, if two cards are drawn without replacement from a deck of cards, the event of drawing a red card on the first trial and that of drawing a red card on the second trial are again not independent.

3. Dependent Events: Two events are dependent if the outcome or occurrence of the first affects the outcome or occurrence of the second so that the probability is changed. 

A card is chosen at random from a standard deck of 52 playing cards. Without replacing it, a second card is chosen. What is the probability that the first card chosen is a queen and the second card chosen is a jack?
Probabilities:			P(queen on first pick)  =   4  52 P(jack on 2nd pick given queen on 1st pick)  =   4  51 P(queen and jack)  =   4   ·   4   =    16    =    4   52 51 2652 663

Sources: http://www.mathsisfun.com/data/probability-events-mutually-exclusive.html.
              http://www.mathgoodies.com/lessons/vo16/dependent_events.html.