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: $\frac{number \ of \ favorable outcomes}{total \ number \ of \ possible \ outcomes}$

Free printable Worksheets

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.

Answers

1) A number is chosen at random from

1

$1$ to

23

$23$ . Find the probability of selecting a

2

$2$ or smaller.

\frac{2}{23}

$\ \color{red}{\frac{2}{23}}$

2) A number is chosen at random from

1

$1$ to

16

$16$ . Find the probability of selecting prime numbers.

\frac{3}{8}

$\ \color{red}{\frac{3}{8}}$

3) A number is chosen at random from

1

$1$ to

46

$46$ . Find the probability of selecting prime numbers.

\frac{7}{23}

$\ \color{red}{\frac{7}{23}}$

4) Bag A contains

9

$9$ red marbles and

5

$5$ green marbles. Bag B contains

3

$3$ black marbles and

8

$8$ 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?

\frac{5}{14}, \frac{3}{11}

$\ \color{red}{\frac{5}{14} \ , \frac{3}{11}}$

5) Bag A contains

23

$23$ red marbles and

5

$5$ green marbles. Bag B contains

1

$1$ black marbles and

9

$9$ 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?

\frac{5}{28}, \frac{1}{10}

$\ \color{red}{\frac{5}{28} \ , \frac{1}{10}}$

6) Bag A contains

16

$16$ red marbles and

7

$7$ green marbles. Bag B contains

8

$8$ black marbles and

2

$2$ 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?

\frac{7}{23}, \frac{4}{5}

$\ \color{red}{\frac{7}{23} \ , \frac{4}{5}}$

7) Bag A contains

17

$17$ red marbles and

9

$9$ green marbles. Bag B contains

7

$7$ black marbles and

6

$6$ 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?

\frac{9}{26}, \frac{7}{13}

$\ \color{red}{\frac{9}{26} \ , \frac{7}{13}}$

8) Bag A contains

24

$24$ red marbles and

7

$7$ green marbles. Bag B contains

5

$5$ black marbles and

9

$9$ 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?

\frac{7}{31}, \frac{5}{14}

$\ \color{red}{\frac{7}{31} \ , \frac{5}{14}}$

9) A number is chosen at random from

1

$1$ to

32

$32$ . Find the probability of selecting prime numbers.

\frac{11}{32}

$\ \color{red}{\frac{11}{32}}$

10) A number is chosen at random from

1

$1$ to

18

$18$ . Find the probability of selecting prime numbers.

\frac{7}{18}

$\ \color{red}{\frac{7}{18}}$

How to Solve Probability Problems