## How to Solve Probability Problems

### 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.

1) A number is chosen at random from $$1$$ to $$23$$. Find the probability of selecting a $$2$$ or smaller. $$\ \color{red}{\frac{2}{23}}$$
2) A number is chosen at random from $$1$$ to $$16$$. Find the probability of selecting prime numbers. $$\ \color{red}{\frac{3}{8}}$$
3) A number is chosen at random from $$1$$ to $$46$$. Find the probability of selecting prime numbers. $$\ \color{red}{\frac{7}{23}}$$
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?$$\ \color{red}{\frac{5}{14} \ , \frac{3}{11}}$$
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?$$\ \color{red}{\frac{5}{28} \ , \frac{1}{10}}$$
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?$$\ \color{red}{\frac{7}{23} \ , \frac{4}{5}}$$
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?$$\ \color{red}{\frac{9}{26} \ , \frac{7}{13}}$$
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?$$\ \color{red}{\frac{7}{31} \ , \frac{5}{14}}$$
9) A number is chosen at random from $$1$$ to $$32$$. Find the probability of selecting prime numbers. $$\ \color{red}{\frac{11}{32}}$$
10) A number is chosen at random from $$1$$ to $$18$$. Find the probability of selecting prime numbers. $$\ \color{red}{\frac{7}{18}}$$

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