## 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:**\(\frac{number \ of \ favorable outcomes}{total \ number \ of \ possible \ outcomes}\)

### Exercises for Probability Problems

**1) **A number is chosen at random from \( 1 \) to \( 23 \). Find the probability of selecting a \( 2 \) or smaller.

**2) **A number is chosen at random from \( 1 \) to \( 16 \). Find the probability of selecting prime numbers.

**3) **A number is chosen at random from \( 1 \) to \( 46 \). Find the probability of selecting prime numbers.

**4) **Bag A contains \( 9 \) red marbles and \( 5 \) green marbles. Bag B contains \( 3 \) black marbles and \( 8 \) orange marbles. What is the probability of selecting a green marble at random from bag A? What is the probability of selecting a black marble at random from Bag B?

**5) **Bag A contains \( 23 \) red marbles and \( 5 \) green marbles. Bag B contains \( 1 \) black marbles and \( 9 \) orange marbles. What is the probability of selecting a green marble at random from bag A? What is the probability of selecting a black marble at random from Bag B?

**6) **Bag A contains \( 16 \) red marbles and \( 7 \) green marbles. Bag B contains \( 8 \) black marbles and \( 2 \) orange marbles. What is the probability of selecting a green marble at random from bag A? What is the probability of selecting a black marble at random from Bag B?

**7) **Bag A contains \( 17 \) red marbles and \( 9 \) green marbles. Bag B contains \( 7 \) black marbles and \( 6 \) orange marbles. What is the probability of selecting a green marble at random from bag A? What is the probability of selecting a black marble at random from Bag B?

**8) **Bag A contains \( 24 \) red marbles and \( 7 \) green marbles. Bag B contains \( 5 \) black marbles and \( 9 \) orange marbles. What is the probability of selecting a green marble at random from bag A? What is the probability of selecting a black marble at random from Bag B?

**9) **A number is chosen at random from \( 1 \) to \( 32 \). Find the probability of selecting prime numbers.

**10) **A number is chosen at random from \( 1 \) to \( 18 \). Find the probability of selecting prime numbers.