Question

example #3 the results of rolling a 6 - sided die are shown in the bar graph below
roll of a die
a) how many times was a 5 rolled?
b) find the experimental probability of rolling a 6. show your answer as a fraction, decimal, and percent
c) find the experimental probability of not rolling a 6

Explanation:

Step1: Analyze the bar graph for part a)

Count the frequency (height of the bar) corresponding to \(5\).

Step2: Calculate experimental probability for part b)

Use the formula \(P(A)=\frac{\text{Number of times }A\text{ occurs}}{\text{Total number of trials}}\).

Step3: Calculate probability for part c)

Use the formula \(P(\text{not }A)=1 - P(A)\)

Answer:

a) Let's assume the height of the bar for \(5\) is \(2\) (since the graph is not clear with exact numbers, but for the sake of showing the method). So the number of times \(5\) was rolled is \(2\).
b) Let's assume the height of the bar for \(6\) is \(3\) and the sum of all bar - heights (total number of trials) is \(3 + 2+1 + 4+2 + 3=15\).

• Fraction: The experimental probability \(P(6)=\frac{3}{15}=\frac{1}{5}\)
• Decimal: \(\frac{1}{5}=0.2\)
• Percent: \(0.2\times100 = 20\%\)

c) The probability of not rolling a \(6\) is \(P(\text{not }6)=1 - P(6)\). Using the values from part b) where \(P(6)=\frac{1}{5}\), then \(P(\text{not }6)=1-\frac{1}{5}=\frac{4}{5}\)