Video: GCSE Mathematics Foundation Tier Pack 2 • Paper 3 • Question 8

GCSE Mathematics Foundation Tier Pack 2 • Paper 3 • Question 8

01:36

Video Transcript

Chuck’s football and his Frisbee are stuck in a tree. Chuck shakes the tree until both items fall out. The probability that the football falls out of the tree first is three-quarters. What is the probability that the Frisbee falls out of the tree first?

The events in this question are an example of what’s known as complementary events. This means that these events cover all possibilities. Either the football falls out of the tree first or the Frisbee falls out first. There are no other possibilities.

A key fact about complementary events is that the sum of their probabilities is always equal to one. For this question, this means that the probability that the football falls out of the tree first plus the probability that the Frisbee falls out of the tree first is equal to one.

We’re told in the question that the probability that the football falls out of the tree first is three-quarters, so we can substitute this value into our equation. Now we just need to solve this equation to find the probability that the Frisbee falls out of the tree first.

It’s a relatively straightforward equation to solve. We just need to subtract three-quarters from each side of the equation, giving the probability that the Frisbee falls out of the tree first is equal to one minus three-quarters. There are four-quarters in one whole, so one minus three-quarters is equal to one-quarter. The probability that the Frisbee falls out of the tree first is one-quarter.

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