Probability measures how likely an event is to occur, expressed as a number between 0 and 1.
0: Impossible
0.5: Even chance
1: Certain
P(E) = Number of favorable outcomes / Total number of outcomes
Rolling a dice:
P(getting 3) = 1/6 ≈ 0.167
P(even number) = 3/6 = 0.5
Sample Space: {Heads, Tails}
P(Heads) = 1/2 = 0.5
P(Tails) = 1/2 = 0.5
Sum: 0.5 + 0.5 = 1 ✓
Standard deck: 52 cards
P(Heart) = 13/52 = 1/4
P(King) = 4/52 = 1/13
P(Red card) = 26/52 = 1/2
P(A or B) = P(A) + P(B) - P(A and B)
For mutually exclusive events: P(A or B) = P(A) + P(B)
P(not A) = 1 - P(A)
The probability that an event doesn't happen
Question 1: A bag contains 5 red balls, 3 blue balls, and 2 green balls. What is the probability of drawing a red ball?
Question 2: Rolling a fair 6-sided dice, what is P(getting a number greater than 4)?
Question 3: If P(sunny) = 0.7, what is P(not sunny)?