Probability - Strengthen your Basics!

Explore equally likely events through a coin toss, defining heads and tails, and learn that the probability of heads or tails is 1/2, with long-run outcomes approaching balance.

Examine equally likely events by counting outcomes on a fair die and computing probability as ways an event can occur over six outcomes, including even and odd results.

Explore how outcomes from a set of seven numbers yield unequal odds: odd numbers occur with probability 4/7, even with 3/7, eight is impossible, and natural numbers are certain.

Explore the probability line where values range from 0 to 1, with 0 impossible and 1 certain, and compare even chances using simple examples.

Explore probability jargon with a dice roll, defining sample space, sample points, and events. Identify outcomes like one or two as the event 'less than three'.

Explore how independent events shape probability in a fair coin toss, showing the 100th outcome remains 1/2 despite prior tails.

Explore how replacement changes probability by contrasting independent and not independent marble draws, showing first red draw (3/6) with and without replacement (3/6 vs 2/5).

Identify independent events where the second event's probability stays the same after the first, and explain mutually exclusive events that cannot occur together.

Explore mutually exclusive events with one throw of a fair dice, compare even and odd outcomes and numbers less than four, and distinguish independent from mutually exclusive events.

Explore probability notations, including P(A ∩ B) for intersection and P(A ∪ B) for union, and contrast independent versus mutually exclusive events.

Explore the intersection and union of events A and B using numbers 1–10 to derive the probability of A and B together (3/10) and A or B (7/10).

Explore intersection in probability by analyzing events A (even numbers) and B (numbers greater than five) among 1–10. Apply P(A∩B)=P(A)×P(B|A), and note independence when P(A∩B)=P(A)P(B).

Explore how the intersection of independent events equals the product of their probabilities, illustrated by coin flip and dice outcomes, yielding 1/12.

The lecture demonstrates union of two events using p(a) + p(b) - p(a and b) with a as even numbers and b as numbers greater than five, yielding 7/10.

Explore the union of mutually exclusive events in probability, using P(A∪B)=P(A)+P(B)-P(A∩B) with A as odds and B as evens from 1–6; union probability equals 1.

Strengthen your basics of probability by applying intersection and independence rules, including P(A∩B)=P(A)P(B) and P(A∪B)=P(A)+P(B)−P(A∩B), illustrated with a coin and dice example yielding 1/12.

Calculate the union probability of a head or a three on a die using P(A or B)=P(A)+P(B)−P(A and B); recognize independence and not mutually exclusive events.

Compute the probability of a sum of eleven when two fair dice are rolled. Treat outcomes (5,6) and (6,5) as mutually exclusive, with independent 1/6 probabilities, yielding 1/18.

Explore probability with two coins tossed together, showing four outcomes and the independence of each coin's result.

Explore all 36 outcomes when two dice are thrown together. The lecture organizes results by d1 and d2 into six columns and highlights their independence.

Examine two-coin probability: one head and tail (2/4) and at least one head (3/4) using one minus the probability of no heads and removing unwanted outcomes from the sample space.

Explore probability with two dice by counting outcomes to find the number of ways to make sums like six, and learn to calculate the probability of sums greater than three.

Use the complement to find the probability: sum greater than three equals one minus sums less than or equal to three, giving eleven twelfths from thirty-six outcomes.