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## How to Practice Probability Questions on the GRE- Part II

Two events are said to be independent if the probability of any one of the event occurring is not affected by the probability of the other event occurring.  If A and B are two independent events then the probability of both occurring is given by:
P (A and B) = P (A) x P (B).

Let’s understand this by solving a problem.

1.  A jar contains 20 coins numbered from one to twenty. Amit selects a coin at random and then replaces it. He then selects another coin at random. What is probability that both the coins will be odd numbered ones?

Solution:

The number of odd numbered coins in the jar = 10.
The total number of coins = 20
The probability of selecting an odd numbered coin the first time = 10/20 = 1/2
Since the first coin that was selected was replaced the number of odd numbered coins and total number of coins do not change when the next coin is selected.
Hence the probability of selecting an odd numbered coins the second time = 10/20 = 1/2

Now P(odd and odd) = P(odd) x P(odd)
= 1/2 x 1/2 = 1/4

Two events are said to be dependent if the probability of any one of the event occurring is affected by the occurring of the other event. If A and B are two dependent events then the probability of both occurring is given by:
P (A and B) = P (A) x P (B).

Let’s understand this by solving a problem.

2.    A jar contains 20 coins numbered from one to twenty. If Bob selects two coins at random one after the other without replacement, what is the probability that both the coins will be odd numbered ones?

Solution:

In the beginning the number of odd numbered coins = 10
Total number of coins in the jar = 20.
Probability of selecting an odd numbered coin the first time = 10/20 = 1/2

After an odd numbered coin is selected and not replaced,

The total number of odd numbered coins currently in the jar = 9
The total number of coins currently in the jar = 19.
Therefore probability of selecting an odd numbered coins the second time = 9/19
Now P (odd and odd) = P (odd) x P (odd)
= 1/2 x 9/19 = 9/38

In our next blog on Probability, we will be seeing more questions on mutually exclusive and non-mutually exclusive events.

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