Need scenario #1: you flip a coin and roll a six sided die. what is the probability that you will flip heads and roll a number greater than 2? scenario #2: you spin a colored wheel and roll a six sided die. the colored wheel has 4 different colors (blue, green, red, and orange). what is the probability that you will spin on blue or roll a 6? • what is the probability for the scenario that gives you the better odds? if you determine that the odds are the same, then document the probability for the either of scenarios.

Scenario #1:

Flipping a coin and rolling a die are independent events, so the combined probability is the product of the individual probabilities.

Flipping a coin: There are two different possible outcomes, heads and tails. You are interested in heads. You are interested in 1 outcome out of 2.

p(heads) = 1/2

Rolling a die: There are 6 different possible outcomes, the numbers 1, 2, 3, 4, 5, and 6. You are interested in a number greater than 2, so your desired outcomes are 3, 4, 5, 6, which means 4 different desired outcomes out of 6.

p(die toss greater than 2) = 4/6 = 2/3

Combined probability:

p(heads followed by number greater than 2) =

= p(heads) * p(die toss greater than 2)

= 1/2 * 2/3

= 1/3

Scenario #2:

There are 4 colors on the spinner. For each color on the spinner, the die can land on one of 6 numbers. 4 * 6 = 24. There are 24 different combined outcomes.

You are interested in blue OR 6. Six outcomes have blue and a number from 1 to 6. Then if the spinner lands in any of the other 3 colors, each one has one outcome of 6 with that color. The total number of desired outcomes is 6 + 3 = 9.

Number of desired outcomes: 9

Number of possible outcomes: 24

p(blue or 6) = 9/24 = 3/8

Final Question:

The scenario that gives you better odds is Scenario #2 since 3/8 > 1/3.