Conditional probability
Edexcel GCSE Maths revision on Conditional probability. Aligned to the Pearson Edexcel GCSE Mathematics 1MA1 specification. This bank has 16 practice questions on this topic.
Sample questions (3 of 16)
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Question 1
A bag contains 3 red balls and 2 blue balls. If one ball is picked at random and not replaced, what is the probability that the second ball is blue given that the first ball was red?
- A) One half because two blue remain from four
- B) Two fifths since two blue exist in the bag
- C) Two fourths as one blue stays in the five
- D) One third as only two blue are inside set
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Answer: One half because two blue remain from four
The correct answer is One half because two blue remain from four. After one red ball is removed, there are 4 balls left in the bag, 2 of which are blue, making the conditional probability 2/4 or 1/2. A common mistake is to ignore that the total number of balls decreases.
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Question 2
In a group of 20 students, 12 study French and 8 study German. If 5 study both, what is the probability that a student studies German given that they study French?
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Answer: 0.417
The correct answer is 0.417 (or 5/12). You divide the number of students studying both languages (5) by the total number of students studying French (12) to find the probability. This represents the proportion of the French group that also falls into the German category.
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Question 3
A fair six-sided die is rolled twice. What is the probability that the second roll is a six given that the first roll was an even number?
- A) One over six since rolls are independent events
- B) One over three as the sample space is reduced
- C) Two over six because the first roll is fixed
- D) Three over six as even numbers include the six
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Answer: One over six since rolls are independent events
The correct answer is One over six since rolls are independent events. Because the die has no memory, the result of the first roll does not influence the probability of the second roll. Many students incorrectly assume the condition changes the second outcome's probability.
Want to test yourself on the remaining cards for this topic?
13 more questions on Conditional probability — plus mistakes tracking and spaced repetition across the whole Maths spec.