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# Probability shortcuts

## Probability  is the  extent or chance to which likely to happen an event.

If an act or an experiment has more than one possible result which is known in advance but unable to predict which result is going to occur first then such experiment is called a random experiment.

Examples of Random Experiment:

1. While tossing a coin, we can’t sure whether a head or tail would come up. The result may be either Head(H) or Tail(T).
2. When two coins are tossed simultaneously we can’t predict the outcomes. Here the probability of results are (H, T), (H, H), (T, H), (T, T).
3. If a six-faced dice is thrown we cant say which number will turn up though we know all the possible outcomes (1,2,3,4,5,6). The result should be any of those numbers.

Sample Space: The set of all possible outcomes or chances of a random experiment is called sample space.

When two dice are thrown simultaneously  Then the sample space (S) = {(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6) }

Thus , The sample space contains 36 sample points.

# Probability Shortcut Tricks:

When two dice are thrown The probability of sample points for the given sum can be known with below logic. Total No. of sample points when two dice are thrown  = (6*6) =36

Question 1: Find the probability to get sum 3 when two dice are thrown simultaneously?

Sol :      P(S)  =  P(3) / P(Total) = 2/36 = 1/13.

Note: ( From the figure we know for sum 3 the probability of sample points are 2)

Question 2: Find the probability to get sum 10  when two dice are thrown simultaneously?

Sol: Probability to get sum 10 = P(10)/P(total )

= 3/36 ( From the figure we know for sum 10 the probability of sample points are 3)

When three dice are thrown The probability of sample points for the given sum can be known with below logic. Example Question: Find the probability to get sum 5  when three dice are thrown simultaneously?

Sol :

Probability to get sum 5 = P(5)/P(total no. of sample points )

= 6/216.

Note: ( From the above figure we know for sum 5 the probability of sample points are 6)