How to Solve Probability Problems

How to Solve Probability Problems

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The Solution for Probability Problems

It is possible to solve a lot of easy probability problems merely by understanding \(2\) basic rules, which are:

• The possibility of any sample point could be in a range of \(0\) to \(1\).
• The total probabilities of all the sample points within a sample space equals \(1\).

Probability of Sample Points

The possibility of a sample point happening is a measure of the possibility sample point will happen.

Example One

Why don’t we do a basic statistical experiment? We’ll flip a coin once. This coin flip could have \(1\) or \(2\) equally-possible outcomes – tails or heads. Together, those results represent the sample space of this experiment. Independently, each of the outcomes stands for a sample point within the sample space. What’s the chances for each sample point?

Solution:

The total of the chances for every sample point has to be \(1\). Plus the chances of acquiring a head is the same as the chances of getting a tail. So, the chances for each sample point (tails or heads) has to be \(\frac{1}{2}\).

Chances for an Event

The chance for an event is a measure of the possibility it will happen. By agreement, statisticians have formed these rules.

• The chances for an event can be in the range of zero to \(1\).
• The chances of event \(A\) is the total of the chances of all the sample points for event \(A\).
• The chance of event \(A\) is shown via \(P(A)\).

So, if event \(A\) weren’t likely to happen, then \(P(A)\) is going to be close to zero. So if event A were quite likely to happen, \(P(A)\) would be near \(1\).

Example two

Let’s pull a card from a deck of poker cards. What’s the chances we’ll get a spade?

Solution:

The sample space for this experiment comprises fifty-two cards, so the chances for each sample point is \(\frac{1}{52}\) . Because there are thirteen spades in a deck, the chances of pulling out a spade is:
\(P(Spade) \ = \ 13 \times \frac{1}{52} \ = \ \frac{1}{4}\)

Conclusion

• Probability is the chance of a future event. It’s shown as a number in-between zero (could not ever happen) to \(1\) (this is going to happen all the time).
• Probability can be shown using fractions, decimals, or percentages.
• To find a solution to a probability problem ascertain the event, and figure out the amount of outcomes for the event, you should utilize probability law: \(\frac{number \ of \ favorable outcomes}{total \ number \ of \ possible \ outcomes}\) 

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