Question

the odds of rolling a 1 on a standard die are 1:5.

what is the probability of getting a 1 upon rolling a die?

a.) \\(\frac{1}{4}\\)

b.) \\(\frac{1}{5}\\)

c.) \\(\frac{5}{1}\\)

d.) \\(\frac{1}{6}\\)

Explanation:

Understand odds in favor

Using the Theoretical Probability knowledge point
The odds in favor of an event are given as the ratio of favorable outcomes to unfavorable outcomes:

$$ \text{Odds} = a:b $$

Here, the odds of rolling a \(1\) are \(1:5\), meaning:

• Favorable outcomes (\(a\)) = \(1\)
• Unfavorable outcomes (\(b\)) = \(5\)

Convert odds to probability

The probability \(P\) of an event occurring is the ratio of favorable outcomes to the total number of possible outcomes:

$$ P = \frac{a}{a + b} $$

Substituting the given values:

$$ P = \frac{1}{1 + 5} = \frac{1}{6} $$

Answer:

• a.) \(\frac{1}{4}\)
• b.) \(\frac{1}{5}\)
• c.) \(\frac{5}{1}\)
• d.) \(\frac{1}{6}\) (Correct answer)