Probability and Statistics
Probability and statistics in Bagrut tests counting, probability rules, conditional probability, and summary statistics. Questions may use a table, a tree, or a word description, and they often ask you to interpret a result rather than only compute it.
Core rules
- P(A∪B)=P(A)+P(B)−P(A∩B); for disjoint events the last term is zero.
- Conditional probability: P(A|B)=P(A∩B)/P(B), provided P(B)>0.
- Independent events satisfy P(A∩B)=P(A)P(B), equivalently P(A|B)=P(A).
- Binomial probability: P(X=k)=C(n,k)p^k(1−p)^(n−k).
- Mean of a data set is the sum divided by n; median is the middle value after ordering; standard deviation measures spread.
- For a normal distribution, convert to z=(x−μ)/σ and use symmetry.
Worked example
A bag has 3 red and 2 blue balls. Two are drawn without replacement. Find the probability that both are red. The first draw is red with probability 3/5. Given that, 2 red and 2 blue remain, so the second is red with probability 2/4=1/2. Multiply: 3/5·1/2=3/10. This is a conditional probability calculation, not two independent draws.
Traps
Using replacement probabilities when the problem says without replacement is the main error. Do not add probabilities of overlapping events without subtracting the intersection. In conditional probability, the denominator is the condition, not the whole sample space. For at least one, the complement is often faster and safer.