ExpertMedium3 marksStructured
AQA GCSE · Question 09.1 · Statistical Measures and Calculations
There are 7 players who can play for a snooker team: Micky, Katie, Niles, Tommo, Paul, Jonno and Emma. Each week four players are needed to make up the team. One week, Micky and Katie are chosen for the team and the other two players are chosen at random. What is the probability that Niles is also in the team?
There are 7 players who can play for a snooker team: Micky, Katie, Niles, Tommo, Paul, Jonno and Emma. Each week four players are needed to make up the team. One week, Micky and Katie are chosen for the team and the other two players are chosen at random. What is the probability that Niles is also in the team?
How to approach this question
1. Determine how many players are left to choose from after Micky and Katie are selected.
2. Determine how many spots are still available on the team.
3. Think about the remaining players as a smaller group. What is the chance of any single player (Niles) being picked to fill one of the available spots?
4. You can think of it as "What is the probability Niles is the first pick?" OR "What is the probability Niles is the second pick?". A simpler way is to consider the proportion of available spots to available players.
Full Answer
After Micky and Katie are chosen, there are 7 - 2 = 5 players remaining.
Two more players need to be chosen from these 5.
The probability of Niles being the first of the two chosen is 1/5.
If he is not chosen first, there are 4 players left for the second spot. The probability of him being chosen second is (4/5) * (1/4) = 1/5.
So the total probability is 1/5 + 1/5 = 2/5.
Alternative method:
There are 5 players left (Niles, Tommo, Paul, Jonno, Emma).
We need to choose 2 more players.
The possible pairs are: (N,T), (N,P), (N,J), (N,E), (T,P), (T,J), (T,E), (P,J), (P,E), (J,E).
There are 10 possible pairs in total (5C2 = 10).
The pairs that include Niles are (N,T), (N,P), (N,J), (N,E). There are 4 such pairs.
The probability is the number of favourable outcomes divided by the total number of outcomes.
P(Niles is chosen) = 4/10 = 2/5.
Answer: 2/5
After Micky and Katie are chosen, the situation is:
- Number of players remaining: 7 - 2 = 5 (Niles, Tommo, Paul, Jonno, Emma).
- Number of team spots to fill: 4 - 2 = 2.
We are choosing 2 players from the remaining 5. Each of the 5 players has an equal chance of being chosen.
A simple way to think about this is that there are 2 available "winning" spots and 5 players competing for them. Therefore, the probability for any one player (like Niles) to be chosen is 2/5.
More formally, using combinations:
- The total number of ways to choose 2 players from the remaining 5 is "5 choose 2" or ⁵C₂ = (5!)/(2! * 3!) = 10.
- The number of ways to choose Niles and one other player is "1 choose 1" (for Niles) multiplied by "4 choose 1" (for the other player), which is 1 * 4 = 4.
- The probability is (Favourable outcomes) / (Total outcomes) = 4/10 = 2/5.
Common mistakes
✗ Calculating the probability based on the original 7 players (e.g., 4/7).
✗ Getting the number of remaining players or spots wrong.
✗ Overcomplicating the calculation. The simple ratio of spots to players (2/5) works directly.
Practice the full AQA GCSE Statistics Higher Tier Paper 2
43 questions · hints · full answers · grading
More questions from this exam
Q01A fair coin is tossed four times. Circle the probability of getting 'tails' on all 4 tosses.EasyQ02Which one of these is **not** a measure of spread?EasyQ03Olivia wants to obtain a systematic sample of size 40 from a population of 2000 competitors in a ...EasyQ04Which statistical term means 'the extent to which something gives results that are consistent'?EasyQ05.1BMI stands for Body Mass Index and is based on your height and mass. Louise and William have this...Easy