Probability
Sample spaces, the addition rule and “at least one”.
Learn with Kutty
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For "A or B", add the chances, then take away the overlap.
Look: A pack of 52: 4 kings, 13 hearts, 1 card is both.
✏️ Your turn!
Type your answer and press Check. Kutty will tell you if it is right.
1P(king or heart)?
2At least one six in two dice rolls?
3P(A) = 0.5, P(B) = 0.3, cannot both happen. P(A or B)?
! Careful!
✗P(king or heart) = 4/52 + 13/52.
✓Take away the king of hearts: 16/52.
✗Listing every case for "at least one".
✓Use 1 − chance of none.
See the whole lesson on one page
For "A or B", add the chances, then take away the overlap.
For "at least one", it is easier to find the chance of none, then take it from 1.
Think of it like thisKings and hearts: the king of hearts is both. Count it once, not twice.
Solved together
Toss 3 coins. What is the chance of at least one head?
The opposite of "at least one head" is "all tails".
½ × ½ × ½ = ⅛Take that from 1.
1 − ⅛ = ⅞
AnswerChance = 7/8.
Now practise it
Kanakku makes new questions on probability every time. It shows the working and gives a hint when you are stuck.