1. Mutually exclusive:-

Two events are 'mutually exclusive' if they cannot occur at the same time. An example is tossing a coin once, which can result in either heads or tails, but not both.

In the coin-tossing example, both outcomes are collectively exhaustive, which means that at least one of the outcomes must happen, so these two possibilities together exhaust all the possibilities. However, not all mutually exclusive events are collectively exhaustive. 

For example, the outcomes 1 and 4 of a single roll of a six sided die are mutually exclusive (cannot both happen) but not collectively exhaustive (there are other possible outcomes; 2,3,5,6).

For example, 

Let A be the event of rolling 4 on a die. What is the probability of not rolling 4?
The probability that we don't roll 4 is equal to 2. Independent event:- Two events are if the occurrence of one has no effect on the occurrence of the other. For instance, if a coin is tossed twice, the outcome of the first toss (heads or tails) has no effect on the outcome of the second toss.

For example,

A dresser drawer contains one pair of socks with each of the following colors: blue, brown, red, white and black. Each pair is folded together in a matching set. You reach into the sock drawer and choose a pair of socks without looking. You replace this pair and then choose another pair of socks. What is the probability that you will choose the red pair of socks both times?

There are a couple of things to note about this experiment. Choosing a pairs of socks from the drawer, replacing it, and then choosing a pair again from the same drawer is a compound event. Since the first pair was replaced, choosing a red pair on the first try has no effect on the probability of choosing a red pair on the second try. Therefore, these events are independent. Solution:-P(red) = 1/5 P(red and red) = P(red) · P(red)                      = 1/ · 1/55                      = 1/25. For example, A coin is tossed and a single 6-sided die is rolled. Find the probability of landing on the head side of the coin and rolling a 3 on the die. Solution:- P(head)  =  1 2 P(3)  =  1 6 P(head and 3)  =  P(head)  ·  P(3) =  1  ·  1 2 6 =   1  12. For example,              Now you know that the probability of heads landing up when you flip a coin is 1/2 What is the probability of getting tails if you flip it again? It is still 1/2 The two events do not affect each other. They are independent. Dependent event:- Two events are dependentifthe occurrence of one event does affectthe occurrence ofthe other(e.g.,randomselection withoutreplacement). Solved Example on Dependent Events Which of the following are dependent events? 1. Getting an even number in the first roll of a number cube and getting an even number in the second roll. 2. Getting an odd number on the number cube and spinning blue color on the spinner. 3. Getting a face card in the first draw from a deck of playing cards and getting a face card in the second draw. (The first card is not replaced.) Solution: Step 1: In (1), rolling a number cube two times are two independent events. Step 2: In (2), rolling an odd number and spinning blue color are two independent events. Step 3: In (3), since the first card is not replaced back, the probability of the second draw depends on the first draw. Step 4: So, the two events in (3) are dependent events. For example, There are 3 red candies left in a bag of multicolored candies with a total of 20 candies left in it. The probability that you will get a red one when you reach in is: 3/20. But what are your chances of getting a red one if you reach in again? There are now 19 candies in the bag, and only two are red. The probability is 2/19. Taking the first candy affected the outcome of the next attempt. The two events are dependent.