in this exercise you are to further examine the concepts of

in this exercise, you are to further examine the concepts of independent events and mutually exclusive events. a) if 2 events are mutually exclusive, determine their joint probability b) if two events with positive probability are independent, explain why their joint probability is not 0. conclude that the 2 events cant be mutually exclusive. c) give an example of 2 events that are neither mutually exclusive nor dependent

Solution

Two events are mutually exclusive if they cannot occur at the same time.

for example: if we toss a coin we cannot get heads and tails at the same time.

a) if 2 events are mutually exclusive their joint probability is zero. (0)

b) When two events are said to be independent of each other, this means

that the probability that one event occurs in no way affects

the probability of the other event occurring.

so here if two independent events A and B are there with positive probabilities

as x and y respectively.

there joint probability is x*y which is not zero.

since the joint probability is not zero, they are not mutually exclusive.

c) suppose you have 2 coins.

event A denotes : getting heads on first coin ,

event B denotes : getting heads on second coin if they are tossed at same time.

here A occurs it doesnot imply that B cannot occur.

so they are not mutually exclusive.

and if A occurs it doesnot change the probability of B occuring.

so they are not dependent.

so we can say here that A and B are neither mutually exclusive nor dependent.