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.
