Mathematics from zero
Probability: multiple-choice review
Six questions that reach across the whole unit. Each one is a small decision: which number, which operation, which rule. Work the arithmetic in your head before you pick — the goal is to choose the right move, not to recite a definition.
Confirm you can read the 0-to-1 scale, compute a probability from favourable over total, choose between multiplying and adding when combining events, take a complement, and tell independent events from dependent ones.
A bag holds 8 marbles, all the same size: 2 are green, 6 are white. You draw one without looking. What is the probability it is green, and why?
You flip a fair coin twice. What is the probability of heads both times, and which operation gives it?
On one roll of a fair die, what is the probability of rolling a 1 or a 6?
A weather model says the probability of rain tomorrow is 0.3. What is the probability of no rain, and what rule are you using?
Which pair of events is independent — one result not affecting the other?
You roll two fair dice. What is the probability that both show a 6, and why does the count come out so small?
The whole unit lives in a few moves. Probability is a number from 0 to 1; for equally likely outcomes it is favourable over total. To combine, ask which question you are answering: both independent events happening multiplies, either of two exclusive events happening adds, and an event not happening is 1 minus its probability. Independence is the test of whether one result changes the other’s possibilities — drawing without replacement breaks it. Pick the operation that matches the question before you do any arithmetic.