Probability Equation Questions worksheet
10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.
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4 marks
A spinner can land on blue, purple, orange or red.
The table shows the probability of each colour.
Colour Blue Purple Orange Red Probability \(x\) \(3x\) \(4x\) \(0.2\) (a)Find the value of \(x\).
(b)The spinner is spun 100 times.
Work out an estimate for the number of times it lands on purple.
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4 marks
A bag contains \(24\) cards. Some of them are red and the rest are black.
Rosa takes a card at random from the bag, records its colour, and puts it back.
She then takes a second card at random from the bag.
The probability that both cards are red is \(\frac{ 361 }{ 576 }\).
(a)Work out how many of the cards in the bag are red.
(b)Find the probability that neither card is red.
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6 marks
A bag contains \(n\) counters.
6 of the counters are red and the other \(n - 6\) counters are blue.
Two counters are taken from the bag at random, without replacement.
The probability that both counters are red is \(\frac{1}{ 3 }\).
(a)Show that \(n^2 - n - 90 = 0\)
(b)Calculate the total number of counters in the bag.
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4 marks
A bag contains 37 counters. Some of the counters are red and the rest are blue.
Two counters are taken from the bag at random, without replacement.
The probability that both counters are red is \(\frac{2}{37}\).
Calculate how many red counters are in the bag.
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4 marks
A bag contains only red counters and green counters.
A counter is taken from the bag at random. The probability that it is red is \(\frac{1}{5}\).
The counter is put back, and then 7 more red counters are put into the bag.
A counter is now taken from the bag at random. The probability that it is red is \(\frac{1}{3}\).
Calculate how many counters were in the bag to start with.
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4 marks
A spinner can land on gold, silver, bronze or grey.
The table shows the probability of each colour.
Colour Gold Silver Bronze Grey Probability \(x\) \(3x\) \(5x\) \(0.55\) (a)Find the value of \(x\).
(b)The spinner is spun 400 times.
Work out an estimate for the number of times it lands on silver.
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4 marks
A bag contains \(19\) tokens. Some of them are gold and the rest are silver.
Anya takes a token at random from the bag, records its colour, and puts it back.
She then takes a second token at random from the bag.
The probability that both tokens are gold is \(\frac{ 49 }{ 361 }\).
(a)Calculate how many of the tokens in the bag are gold.
(b)Calculate the probability that neither token is gold.
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6 marks
A bag contains \(n\) counters.
7 of the counters are red and the other \(n - 7\) counters are blue.
Two counters are taken from the bag at random, without replacement.
The probability that both counters are red is \(\frac{1}{ 11 }\).
(a)Show that \(n^2 - n - 462 = 0\)
(b)Calculate the total number of counters in the bag.
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4 marks
A bag contains 23 counters. Some of the counters are red and the rest are blue.
Two counters are taken from the bag at random, without replacement.
The probability that both counters are red is \(\frac{5}{23}\).
Calculate how many red counters are in the bag.
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4 marks
A bag contains only red counters and green counters.
A counter is taken from the bag at random. The probability that it is red is \(\frac{2}{5}\).
The counter is put back, and then 8 more red counters are put into the bag.
A counter is now taken from the bag at random. The probability that it is red is \(\frac{1}{2}\).
Calculate how many counters were in the bag to start with.
Answers
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(a) \(0.1\)
(b) \(30\) -
(a) \(19\ \text{cards}\)
(b) \(\frac{25}{576}\) -
(a) \(n^2 - n - 90 = 0\)
(b) \(10\) - \(9\)
- \(35\)
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(a) \(0.05\)
(b) \(60\) -
(a) \(7\ \text{tokens}\)
(b) \(\frac{144}{361}\) -
(a) \(n^2 - n - 462 = 0\)
(b) \(22\) - \(11\)
- \(40\)