Step 1

1. Theoretical probability is probability that is determined on the basis of reasoning.

2. a) picking the 9 of clubs from a deck of cards \(\displaystyle{\frac{{{1}}}{{{52}}}}{\left({\frac{{t}}{{i}}}{o}{n}\right)}\)

b) flipping heads with a coin \(\displaystyle{\frac{{{1}}}{{{2}}}}={0.5}{\left({d}{e}{c}{i}{m}{a}{l}\right)}\)

c) picking a diamond from a deck of cards choose 13 form 52. Which is \(\displaystyle{25}\%{\left({p}{e}{r}{c}{e}{n}{t}\right)}\)

d) rolling a 3 with 1 die \(\displaystyle{\frac{{{1}}}{{{6}}}}{\left({\frac{{t}}{{i}}}{o}{n}\right)}\)

e) rolling an even number with 1 die \(\displaystyle{\frac{{{3}}}{{{6}}}}={0.50}{\left({d}{e}{c}{i}{m}{a}{l}\right)}\)

f) flipping heads or tails with a coin \(\displaystyle{100}\%{\left({p}{e}{r}{c}{e}{n}{t}\right)}\)

Step 2

Experimental probability is probability that is determined on the basis of the results of an experiment repeated many times.

1. Theoretical probability is probability that is determined on the basis of reasoning.

2. a) picking the 9 of clubs from a deck of cards \(\displaystyle{\frac{{{1}}}{{{52}}}}{\left({\frac{{t}}{{i}}}{o}{n}\right)}\)

b) flipping heads with a coin \(\displaystyle{\frac{{{1}}}{{{2}}}}={0.5}{\left({d}{e}{c}{i}{m}{a}{l}\right)}\)

c) picking a diamond from a deck of cards choose 13 form 52. Which is \(\displaystyle{25}\%{\left({p}{e}{r}{c}{e}{n}{t}\right)}\)

d) rolling a 3 with 1 die \(\displaystyle{\frac{{{1}}}{{{6}}}}{\left({\frac{{t}}{{i}}}{o}{n}\right)}\)

e) rolling an even number with 1 die \(\displaystyle{\frac{{{3}}}{{{6}}}}={0.50}{\left({d}{e}{c}{i}{m}{a}{l}\right)}\)

f) flipping heads or tails with a coin \(\displaystyle{100}\%{\left({p}{e}{r}{c}{e}{n}{t}\right)}\)

Step 2

Experimental probability is probability that is determined on the basis of the results of an experiment repeated many times.