Question

2.6: probability calculations
probability of simple events
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 shot? (decimal)
4. which of the above questions are about theoretical probability? ______

Explanation:

Step1: Probability of rolling a 5 on a 6 - sided die

The formula for probability is $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. For a 6 - sided die, the total number of outcomes $n = 6$ (the numbers 1, 2, 3, 4, 5, 6). The number of favorable outcomes (rolling a 5) $m = 1$. So $P=\frac{1}{6}$.

Step2: Probability of being on - time

The probability of an event and its complement (opposite) sum to 1. If the probability of being late $P(\text{late})=0.1$, then the probability of being on - time $P(\text{on - time})=1 - P(\text{late})$. So $P(\text{on - time})=1 - 0.1=0.9 = 90\%$.

Step3: Probability of missing a shot

If a player makes 3 out of 7 shots, the number of missed shots is $7 - 3=4$. Using the probability formula $P=\frac{\text{Number of missed shots}}{\text{Total number of shots}}=\frac{4}{7}\approx0.57$.

Step4: Theoretical probability

Theoretical probability is based on the assumption of equally likely outcomes (not on experimental data). Question 1 (rolling a die, all faces are equally likely) and Question 2 (assuming only two states: late or on - time, and using a given probability value without experimental trials) are about theoretical probability. Question 3 is based on the player's past performance (experimental data).

Answer:

1. $\frac{1}{6}$
2. $90\%$
3. $\frac{4}{7}\approx0.57$
4. Questions 1 and 2