Question

1-59 write \theoretical\ or \experimental\ to describe the probabilities of the following situations. a) the chance of getting tails when flipping a coin is \\(\frac{1}{2}\\). ____ b) i flipped a coin eight times and got heads six times, so the probability is \\(\frac{6}{8}\\). __ c) my mom packed my lunch three of the past five days, so the probability that my mom will pack my lunch is \\(\frac{3}{5}\\). __ d) the chance of winning the state lottery is 1 in 98,000,000. __ e) based on mathematical models, the chance of rain today is 60%. __ f) lena got three hits in her last seven times at bat, so her chance of getting a ____

Explanation:

Part a)

Step1: Recall theoretical probability

Theoretical probability is based on the nature of the event (e.g., a fair coin has 2 sides, so probability of tails is $\frac{1}{2}$ without experimentation).

Step2: Classify the situation

The probability of getting tails on a coin flip is derived from the concept of a fair coin (2 possible outcomes, 1 favorable), so it's theoretical.

Step1: Recall experimental probability

Experimental probability is based on actual trials/experiments (flipping the coin 8 times and counting heads).

Step2: Classify the situation

The probability is calculated from 8 coin flips (an experiment), so it's experimental.

Step1: Recall experimental probability

Experimental probability uses past observations (3 out of 5 days mom packed lunch).

Step2: Classify the situation

The probability is based on 5 days of observation (an experiment), so it's experimental.

Answer:

theoretical

Part b)