Probability of single and combined events

When a question asks "how many times" or "estimate the number", multiply the probability by the number of trials — the probability alone is not the answer. E.g. $P=0.15$ over $400$ trials gives an expected $0.15\times400=60$, not $0.15$.

When two remaining outcomes are equally likely, first subtract ALL the given probabilities from $1$, THEN halve the result — do not just halve the given total. E.g. if $0.3+0.1+0.1$ are given, each missing one is $\dfrac{1-0.5}{2}=0.25$.

A probability can never exceed $1$. Adding the probabilities of events that can happen together (overlapping events) double-counts the overlap and can give a value above $1$ — a sign of an error. Only add probabilities for MUTUALLY EXCLUSIVE outcomes, and check the total is at most $1$.

To find a single missing probability, subtract the given ones from $1$: $P(\text{missing})=1-(\text{sum of the rest})$. Adding the given probabilities together instead gives the wrong outcome. E.g. with $P=0.35$ and $P=0.2$ given, the missing one is $1-0.35-0.2=0.45$.

For mutually exclusive events, $P(A\text{ or }B)=P(A)+P(B)$ — you ADD. Multiplying is for "and" with independent events, not for "or". E.g. with $P(1)=0.1$ and $P(2)=0.25$, $P(1\text{ or }2)=0.1+0.25=0.35$, not $0.1\times0.25$.