Probability

dice 


Basics
Probability is the chance that an event will occur.

Probability can be expressed as a fraction, decimal, or percent.

\bf\displaystyle{Probability\,of\,Simple\,Event} = \bf\displaystyle\frac{Number\,of\,Events}{Number\,of\,Possible\,Events}
• The TI-30XS MultiView Scientific Calculator may or may not be needed here.
• Calculator Not Needed: Probability of rolling a five on a single die = \bf\displaystyle\frac{1}{6}
• Calculator Needed: Probability of picking 12 orange balls out of a total of 100 balls, the rest of which are not orange =\bf\displaystyle\frac{12}{100} = \bf\displaystyle\frac{3}{25}
• When asked to convert a fraction to decimal form, use the toggle button toggle .

\bf\displaystyle{Probability\,of\,Compound\,Event} = \bf\displaystyle{Probability\,of\,Multiple\,Events}
• The calculator is usually needed here.
• To arrive at the answer, multiply the probabilities.
• When fractions are multiplied, the answer will be in fraction form.
-> Probability of rolling 1 followed by 2 with a die  = \bf\displaystyle\frac{1}{6} × \bf\displaystyle\frac{1}{6} = \bf\displaystyle\frac{1}{36}
• When percents are multiplied, the answer will be in decimal form.
-> Probability of snow 40% on Monday followed by 60% on Tuesday = 40% × 60% = 0.24
• When asked to convert a decimal to percent form, move the decimal point two places to the right.
-> 0.24 = 24.% = 24%


Formulas (NOT provided by Mathematics Formula Sheet)

\bf\displaystyle{Probability\,of\,Simple\,Event} = \bf\displaystyle\frac{Number\,of\,Events}{Number\,of\,Possible\,Events}

\bf\displaystyle{Probability\,of\,Compound\,Event} = \bf\displaystyle{Probability\,of\,Multiple\,Events}


Question
When rolling a single die from a pair of dice, there are six possible outcomes: 1 or 2 or 3 or 4 or 5 or 6.  In fractional terms, when a die is rolled, what is the probability of a 2?

Answer
\bf\displaystyle\frac{1}{6}

Answer Process
What is the probability of a simple event?
What is the probability of one out of six possible events?
Calculator not needed.
\bf\displaystyle\frac{1}{6}


Question
In fractional terms, what is the probability of picking 24 orange balls out of a total of 100 balls, the rest of which are not orange?

Answer
\bf\displaystyle\frac{6}{25}

Answer Process
What is the probability of a simple event?
What is the probability of 24 out of 100 possible events?
Calculator needed.
\bf\displaystyle\frac{6}{25}

Calculator Click What You See Comment
clear blinker clears screen
fraction 24 down 100 right \bf\displaystyle\frac{24}{100} Simple Event
enter \bf\displaystyle\frac{6}{25} Answer
Probability


Question
With reference to the question above, express your answer in decimal form.

Answer
0.24

Answer Process
See Toggle.
\bf\displaystyle\frac{6}{25} ⇔ 0.24

Calculator Click What You See Comment
clear blinker clears screen
fraction 24 down 100 right \bf\displaystyle\frac{24}{100} Simple Event
enter \bf\displaystyle\frac{6}{25}
toggle 0.24 Answer
(Toggle)
Probability


Question
With reference to the question above, express your answer in percent form.

Answer
24%

Answer Process
See Percent.
To convert a decimal to percent, move the decimal point two places to the right.
0.24 = 24.% = 24%


Question
When rolling a single die from a pair of dice, there are six possible outcomes: 1 or 2 or 3 or 4 or 5 or 6.  In fractional terms, when a die is rolled, what is the probability of rolling a 2 followed by 5?

Answer
\bf\displaystyle\frac{1}{36}

Answer Process
What is the probability of a compound event?
Multiply the probabilities.
\bf\displaystyle\frac{1}{6} × \bf\displaystyle\frac{1}{6}\bf\displaystyle\frac{1}{36}

Calculator Click What You See Comment
clear blinker clears screen
fraction 1 down 6 right ×
fraction 1 down 6 right
\bf\displaystyle\frac{1}{6}\bf\displaystyle\frac{1}{6} Compound Event
enter \bf\displaystyle\frac{1}{36} Answer
Probability


Question
With reference to the question above, express your answer in decimal form.

Answer
0.027777778

Answer Process
See Toggle.
\bf\displaystyle\frac{1}{36} ⇔ 0.027777778

Calculator Click What You See Comment
clear blinker clears screen
fraction 1 down 6 right ×
fraction 1 down 6 right
\bf\displaystyle\frac{1}{6}\bf\displaystyle\frac{1}{6} Compound Event
enter \bf\displaystyle\frac{1}{36}
toggle 0.027777778 Answer
(Toggle)
Probability


Question
With reference to the question above, express your answer in percent form.

Answer
2.777777778%

Answer Process
See Percent.
To convert a decimal to percent, move the decimal point two places to the right.
0.027777778 = 2.7777778%


Question

With reference to the question above, round your answer to the nearest hundredth.

Answer
2.78%

Answer Process
See Rounding.
2.7777778%  2.78%


Question

The probability of snow is 65% on Friday, 75% on Saturday, 55% on Sunday, and 85% on Monday.  In percent terms, rounded to the nearest tenth, what is the probability of snow on all four days?

Answer
22.8%

Answer Process
What is the probability of a compound event?
Multiply the probabilities.
65% × 75% × 55% × 85% = 0.22790625
To convert a decimal to percent, move the decimal point two places to the right.
0.22790625 = 22.790625%  (See Percent.)
Round to the nearest tenth.
22.790625%  22.8%  (See Rounding.)

Calculator Click What You See Comment
clear blinker clears screen
65 2nd % ×
75 2nd % ×
55 2nd % ×
85 2nd % ×
65%*75%*55%*85% Compound Event
enter 0.22790625 Answer
(before percent and rounding)
Probability


Practice – Questions
1.  When flipping a coin, there are two possible outcomes: heads or tails.  In fractional terms, when a coin is flipped, what is the probability of flipping heads?

2.  When flipping a coin, there are two possible outcomes: heads or tails.  In fractional terms, when a coin is flipped, what is the probability of flipping tails?

3.  When flipping a coin, there are two possible outcomes: heads or tails.  In fractional terms, when a coin is flipped, what is the probability of flipping heads followed by heads?

4.  When flipping a coin, there are two possible outcomes: heads or tails.  In fractional terms, when a coin is flipped, what is the probability of flipping tails followed by tails?

5.  When flipping a coin, there are two possible outcomes: heads or tails.  In fractional terms, when a coin is flipped, what is the probability of flipping heads followed by tails?

6.  When flipping a coin, there are two possible outcomes: heads or tails.  In fractional terms, when a coin is flipped, what is the probability of flipping tails followed by heads?

7.  When flipping a coin, there are two possible outcomes: heads or tails.  In decimal terms, when a coin is flipped, what is the probability of flipping heads followed by tails?

8.  When flipping a coin, there are two possible outcomes: heads or tails.  In percent terms, when a coin is flipped, what is the probability of flipping heads followed by tails?

9.  When flipping a coin, there are two possible outcomes: heads or tails.  In percent terms, rounded to the nearest tenth, when a coin is flipped, what is the probability of flipping heads followed by heads followed by heads followed by heads?

10.  The probability of precipitation is 55% on Friday, 65% on Saturday, and 45% on Sunday.  In percent terms, rounded to the nearest hundredth, what is the probability of precipitation on all three days?


Practice – Answers
1.  \bf\displaystyle\frac{1}{2}

2.  \bf\displaystyle\frac{1}{2}

3.  \bf\displaystyle\frac{1}{4}

4.  \bf\displaystyle\frac{1}{4}

5.  \bf\displaystyle\frac{1}{4}

6.  \bf\displaystyle\frac{1}{4}

7.  0.25

8.  25%

9.  6.3%

10.  16.09%

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