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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% 0\% to 100%, 100\%, or a fraction ((between 00 to 1).1).

For example, if you roll a single standard die, the probability of an even number is exactly 50% 50\% or 12 \frac{1}{2} since, of the 66 possible outcomes for what might be rolled, 33 are even and 33 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% 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 11 to 6)6) while Zeke throws a standard eight-sided die ((marked from 11 to 8).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 mean predicting sun and tails mean 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 5252 cards — 2626 red and 2626 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 11 to 8).8).
  • However, Anela now throws a non-standard six-sided die that is marked from 22 to 77.

Which of these events are more likely to occur?

  • Zeke throws a larger number than Anela.

  • Zeke throws a smaller number than Anela.

Test Your Probabilistic Intuition


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