### Probability Fundamentals

A probability is the measurement of what chance some specified outcome has for happening. Probabilities are typically either expressed as a percentage, measured from $0\%$ to $100\%,$ or a fraction (between $0$ to $1).$

For example, if you roll a single standard die, the probability of an even number is exactly $50\%$ or $\frac{1}{2}$ since, of the 6 possible outcomes for what might be rolled, 3 are even and 3 are odd.

For the problems in this sequence, your job is to intuit if the event that's specified is less than, more than, or exactly 50% likely to occur. These next five questions are meant only to test your intuition, but you can find the complete explanations if you're curious. We'll move on and introduce how to calculate probabilities numerically in the next two sets of challenges!

# Test Your Probabilistic Intuition

Anela throws a standard six-sided die (marked from 1 to 6) while Zeke throws a standard eight-sided die (marked from 1 to 8).

The probability Zeke throws a larger number than Anela is $\text{\_\_\_\_\_\_\_\_\_\_}.$

# Test Your Probabilistic Intuition

You throw a pair of fair coins. The probability that the result is either both are heads or both are tails is $\text{\_\_\_\_\_\_\_\_\_\_}.$

# Test Your Probabilistic Intuition

In the region where Cormac lives, it is sunny three-quarters of the days and rains for the rest.

Every day Cormac makes a weather prediction by flipping a fair coin; heads means predicting sun and tails means predicting rain.

The probability Cormac will correctly predict the weather this way on a particular day is $\text{\_\_\_\_\_}.$

# Test Your Probabilistic Intuition

A standard deck with 52 cards — 26 red and 26 black — is shuffled.

The probability that the top card is the same color as the bottom card is $\text{\_\_\_\_\_\_\_\_\_\_}.$

# Test Your Probabilistic Intuition

Let's modify the problem you saw earlier with Anela and Zeke slightly:

• Zeke still throws a standard eight-sided die (marked from 1 to 8).
• However, Anela now throws a non-standard six-sided die that is marked from 2 to 7.

The probability Zeke throws a larger number than Anela is $\text{\_\_\_\_\_\_\_\_\_\_}.$

# Test Your Probabilistic Intuition

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