Question

probability of an event happening = \frac{number of ways it can happen}{total number of outcomes}

1. what is the probability of rolling a 5 on a 6 - sided die? (fraction)
2. if your probability of being late to school is 10%, how likely are you to be on time? (percent)
3. if a basketball player typically makes 3 out of 7 shots, what is her probability of missing a s

(decimal)

Explanation:

Step1: Calculate probability for rolling a 5

A 6 - sided die has 6 possible outcomes (\(1,2,3,4,5,6\)). There is 1 way to roll a 5.
Using the formula \(P=\frac{\text{Number of ways it can happen}}{\text{Total number of outcomes}}\), we have \(P = \frac{1}{6}\).

Step2: Calculate probability of being on time

The probability of being late is \(10\%=0.1\). The sum of the probability of being late (\(P_{late}\)) and the probability of being on time (\(P_{on - time}\)) is \(1\) (or \(100\%\)).
So \(P_{on - time}=1 - P_{late}\). Substituting \(P_{late}=0.1\), we get \(P_{on - time}=1 - 0.1=0.9 = 90\%\).

Step3: Calculate probability of missing a shot

The probability of making a shot is \(P_{make}=\frac{3}{7}\). The sum of the probability of making a shot (\(P_{make}\)) and the probability of missing a shot (\(P_{miss}\)) is \(1\).
So \(P_{miss}=1-\frac{3}{7}=\frac{7 - 3}{7}=\frac{4}{7}\approx0.57\) (rounded to two decimal places).

Answer:

1. \(\frac{1}{6}\)
2. \(90\%\)
3. \(0.57\)