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Flashcards: Find probabilities

What is the probability that a person will roll an even number on a six-sided fair die?

$50\%$ $\displaystyle 50\%$

$40\%$ $\displaystyle 40\%$

$22\%$ $\displaystyle 22\%$

$13\%$ $\displaystyle 13\%$

$33\%$ $\displaystyle 33\%$

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Flashcards: Find probabilities

What is the probability that a person will roll an even number on a six-sided fair die?

$50\%$ $\displaystyle 50\%$

$40\%$ $\displaystyle 40\%$

$22\%$ $\displaystyle 22\%$

$13\%$ $\displaystyle 13\%$

$33\%$ $\displaystyle 33\%$

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Flashcards: Find probabilities

What is the probability that a person will roll an even number on a six-sided fair die?

Your answer:

$40\%$ $\displaystyle 40\%$

Your answer:

$22\%$ $\displaystyle 22\%$

Your answer:

$13\%$ $\displaystyle 13\%$

Your answer:

$33\%$ $\displaystyle 33\%$

Correct answer:

$50\%$ $\displaystyle 50\%$

Explanation:

In order to solve this problem, we need to discuss probabilities. A probability is generally defined as the chances or likelihood of an event occurring. It is calculated by identifying two components: the event and the sample space. The event is defined as the favorable outcome or success that we wish to observe. On the other hand, the sample space is defined as the set of all possible outcomes for the event. Mathematically we calculate probabilities by dividing the event by the sample space:

$P=\frac{\textup{event: particular phenomenon we wish to observe}}{\textup{sample space: total number of possible outcomes}}$

The die has six sides with the following values: one tow, three, four, five, and six. Of these values the die has three that are even: two, four, and six. We can write the following probability.

$P=\frac{3\textup{ even values}}{6\textup{ total possible outcomes}}$

Simplify.

$P=\frac{3}{6}$ $\displaystyle P=\frac{3}{6}$

$P=\frac{1}{2}$ $\displaystyle P=\frac{1}{2}$

Now, let's convert this into a percentage:

$\frac{1}{2}=0.5$ $\displaystyle \frac{1}{2}=0.5$

$0.5\times100\%=50\%$ $\displaystyle 0.5\times100\%=50\%$

Flashcards: Find probabilities

Two fair dice are tossed. You are not shown the dice but you are told that exactly one die shows an even number. Give the probability that a total of seven was thrown.

$\frac{2}{9}$ $\displaystyle \frac{2}{9}$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\frac{1}{6}$ $\displaystyle \frac{1}{6}$

$\frac{4}{9}$ $\displaystyle \frac{4}{9}$

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

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Flashcards: Find probabilities

Two fair dice are tossed. You are not shown the dice but you are told that exactly one die shows an even number. Give the probability that a total of seven was thrown.

Your answer:

$\frac{2}{9}$ $\displaystyle \frac{2}{9}$

Your answer:

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

Your answer:

$\frac{1}{6}$ $\displaystyle \frac{1}{6}$

Your answer:

$\frac{4}{9}$ $\displaystyle \frac{4}{9}$

Correct answer:

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

Explanation:

Two fair dice can be thrown with 36 equally probable rolls. 18 rolls comprise one even number and one odd number. They are as follows - with the rolls that total seven in boldface:

$1\textup{-}2, 1\textup{-}4, \textbf{1-6}, 2\textup{-}1, 2\textup{-}3, \textbf{2-5}, 3\textup{-}2, \textbf{3-4}, 3\textup{-}6,$

$4\textup{-}1, \textbf{4-3}, 4\textup{-}5, \textbf{5-2}, 5\textup{-}4, 5\textup{-}6, \textbf{6-1}, 6\textup{-}3, 6\textup{-}5.$

6 of the 18 possible rolls have total 7, making the probability of a roll of 7, given that exactly one doe shows an even number, equal to $\frac{6}{18} = \frac{1}{3}$ $\displaystyle \frac{6}{18} = \frac{1}{3}$ .

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Flashcards: Find probabilities

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Flashcards: Find probabilities

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Flashcards: Find probabilities

Flashcards: Find probabilities

Flashcards: Find probabilities

Flashcards: Find probabilities

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