MediumMathematicsHigh School (11–12)Statistics and Probability › ProbabilityNumerical

For two events of an experiment, P(A) = 0.6, P(B) = 0.45 and P(A ∪ B) = 0.8…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

For two events of an experiment, $P(A) = 0.6$ , $P(B) = 0.45$ and $P(A \cup B) = 0.8$ . Find $P(A \cap B)$ . Then find the probability that $A$ happens and $B$ does not, the probability that exactly one of them happens, and the probability that neither happens.

Need a reminder? The key ideaShow

$P(A \cup B) = P(A) + P(B) - P(A \cap B)$ . Exactly one of $A$ and $B$ has probability $P(A) + P(B) - 2P(A \cap B)$ , and neither has probability $1 - P(A \cup B)$ . For three events: singles, minus pairs, plus triple.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

← All Problems

← A card is drawn at random from an ordinary pack of 52 cards…A number is chosen at random from the whole numbers 1 to 60… →

More onStatistics and Probability › Probability

Discussion (0)

Loading…