Question

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

Answer 1

Answer:

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

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

Step-by-step 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:

$Games=\frac{1 \ game}{p(goal)}\\\\=\frac{1}{0.36}\\\\=2.778\approx 3$

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:

$C_g=0.15\times 600\\\\=\£90$

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:

$t=\frac{Balance}{Rate}\\\\=\frac{600-90}{20}\\\\=\frac{510}{20}\\\\=25.5\approx 26$

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

$100\%=\frac{540}{0.1}\\\\=\£5400$

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

$=540\times 10\\\\=\£5400$

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:

$P(Each \ Color)=P(Yellow)=\frac{1}{10}\\\\\therefore P(Yellow)$

Hence, this is impossible since 0.10<0.35