Video: AQA GCSE Mathematics Foundation Tier Pack 2 β€’ Paper 1 β€’ Question 13

Jane and Anne are playing catch. Jane either catches the ball with one hand, catches it with two hands, or does not catch it. The probability that Jane catches the ball with one hand is 0.2. The probability that Jane catches the ball with two hands is 0.5. Work out the probability that Jane does not catch the ball.

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Video Transcript

Jane and Anne are playing catch. Jane either catches the ball with one hand, catches it with two hands, or does not catch it. The probability that Jane catches the ball with one hand is 0.2. The probability that Jane catches the ball with two hands is 0.5. Work out the probability that Jane does not catch the ball.

There are three possible outcomes in this question. Either Jane catches the ball with one hand, catches it with two hands, or does not catch it. We know that, in probability, the sum of all outcomes equals one. We were told in the question that the probability that Jane catches the ball with one hand is 0.2. The probability that she catches the ball with two hands is 0.5. We have been asked to work out the probability that Jane does not catch the ball. We will call this 𝑝.

As the sum of all outcomes is equal to one, we can set up an equation. 0.2 plus 0.5 plus 𝑝 is equal to one. The probability that she catches it with one hand, two hands, or does not catch it add up to one.

Our first step here is to group or collect the like terms on the left-hand side. We need to add 0.2 and 0.5. 0.2 plus 0.5 is 0.7. This gives us 0.7 plus 𝑝 is equal to one. Finally, in order to calculate 𝑝, we need to subtract 0.7 from both sides of the equation. 0.7 minus 0.7 is zero. Therefore, on the left-hand side, we’re left with 𝑝. One minus 0.7 is equal to 0.3. Therefore, 𝑝 equals 0.3. The probability that Jane does not catch the ball is 0.3.

We could also have solved this problem using fractions or percentages. The sum of all outcomes must equal 100 percent. 0.2 is the same as 20 percent. 0.5 is the same as 50 percent. These two percentages sum to 70 percent. This means that the percentage that is left over, the probability that she does not catch it, is 30 percent. And 30 percent is equal to or equivalent to 0.3.

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