If an element cannot be selected again after being selected once, we say that we did sampling without replacement. For example when we pick out a ball from a jar containing five balls of different colors and put it aside instead of placing it back in the same jar. Then pick out the second ball from the jar in the same way and continue this process until the last ball, then the probability of the first ball will be 1/5; the probability of the 2nd ball will be 1/4, the probability of the 3rd ball will be 1/3, the probability of the 4th ball will be 1/2 while the probability of 5th ball will be 1.
We see here that the probability of every next ball varies as we pick out more and more balls from the jar. In other words, as the total number of balls in the jar decreases their probability of being selected increase. Here each event, picking a ball from the jar, has an effect upon subsequent events. So we can say that they are not independent and mutually exclusive of each other and their covariance is not equal to zero. For sampling with replacement click here.
