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# AQA A-level Maths Dependent outcomes

In probability, a set of events are exhaustive if at least one of the events must occur.

In probability, two events are mutually exclusive if they cannot both occur at the same time.

One event happening can change the probability that a second event happens. We must use the correct probability for the second event based on the outcome of the first event.

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A football player is awarded a penalty in a game. If he scores the penalty, the probability that they win the game is 7/10. If he misses the penalty, the probability that they win the game is 1/5. The probability he scores the penalty is 1/2. What is the probability he scores the penalty and they do not win the game?

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# ✅

A shop is selling pens. They have 60 pens in stock: 33 blue and 27 black. If someone randomly picks 2 of the pens (without replacing the 1st), what is the probability that they are both black?

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