Question

A famous Premier-league footballer was quoted on Match of the Day to have a goal-scoring statistic of 0.36

(a) Can you briefly explain what that might mean?

(b) How many games would he have to play to score a whole number of goals?

The approximate cost of a Maths GCSE exam retake is £600.

(a) What is 15% of this fee?[1]

(b) The government agrees to pay the deposit, providing the student agrees to pay the outstanding balance. If the student pays the fee at £20 per week, how many weeks will be needed to pay the balance?[2]

(c) Another student is told that the level 2 Maths exam is priced at a 10% discount of £450. How much would the course cost without the discount?[2]

15. A bag contains 10 coloured beads. Raj claims that the probability
of drawing out a yellow is 0.35. Use a simple calculation to show that this is not possible [2]

Answer 1

`13a.\ The \ probability\ of \ scoring\ a\ goal\ in\ a\ game\ is\ 0.36\\\\b. 3 \ games`

14.

`a. \ \£90\\b. \ 26 \ weeks\\c. \ \£4,860`

15. This is not possible since p(yellow)=0.10 which is less than the stated 0.35

Explanation:

13 a. -A goal-scoring statistic is the probability of a player scoring one goal in any given game played.

-A 0.36 goal scoring statistic means that the player has a 0.36 or 36% chance of scoring a goal in any game that he is involved in.

b. To determine the number of games it takes to score a whole goal, we divide the probability by 1 goal:

`Games=(1 \ game)/(p(goal))\\\\=(1)/(0.36)\\\\=2.778\approx 3`

Hence, it takes approximately 3 games to score a full goal.

14.-The cost of a GCSE retake is £600 and attracts a 15% deposit

#The 15% equivalent in actual pounds is calculated by multiplying the percentage by the total cost as:

`C_g=0.15* 600\\\\=\£90`

Hence, the 15% deposit amount equals £90

b.#The student pays the balance in a £20 per week scheme,the total number of weeks is calculated as:

`t=(Balance)/(Rate)\\\\=(600-90)/(20)\\\\=(510)/(20)\\\\=25.5\approx 26`

Hence, it takes 26 weeks to clear the balance.

c. Given that 10% is the equivalent of £450

-We divide this amount by 10% to get the 100% equivalent

#We know that 10%=0.10

`100\%=(540)/(0.1)\\\\=\£5400`

#Alternatively, 100% divided by 10% is 10. Multiply this value by £540:

`=540* 10\\\\=\£5400`

We subtract the discount amount for the per-discount price:

`Cost=Total -discount\\\\=5400-540\\\\=\£4860`

Hence, it will cost £4,860 without the discount.

15. Since we are not given the proportion of colors in the bag, we assume that all the 10 beads have different colors.

-As such, the sample space is 10 and each color has an equal chance of being picked:

`P(Each \ Color)=P(Yellow)=(1)/(10)\\\\\therefore P(Yellow)<0.35\\\\0.10<0.35`

Hence, this is impossible since 0.10<0.35