Answer:
![13a.\ The \ probability\ of \ scoring\ a\ goal\ in\ a\ game\ is\ 0.36\\\\b. 3 \ games](https://tex.z-dn.net/?f=13a.%5C%20%20The%20%5C%20probability%5C%20of%20%5C%20scoring%5C%20a%5C%20%20goal%5C%20%20in%5C%20%20a%5C%20%20game%5C%20%20is%5C%20%200.36%5C%5C%5C%5Cb.%203%20%5C%20games)
14.
![a. \ \£90\\b. \ 26 \ weeks\\c. \ \£4,860](https://tex.z-dn.net/?f=a.%20%5C%20%5C%C2%A390%5C%5Cb.%20%5C%2026%20%5C%20weeks%5C%5Cc.%20%5C%20%5C%C2%A34%2C860)
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](https://tex.z-dn.net/?f=Games%3D%5Cfrac%7B1%20%5C%20game%7D%7Bp%28goal%29%7D%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B0.36%7D%5C%5C%5C%5C%3D2.778%5Capprox%203)
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](https://tex.z-dn.net/?f=C_g%3D0.15%5Ctimes%20600%5C%5C%5C%5C%3D%5C%C2%A390)
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](https://tex.z-dn.net/?f=t%3D%5Cfrac%7BBalance%7D%7BRate%7D%5C%5C%5C%5C%3D%5Cfrac%7B600-90%7D%7B20%7D%5C%5C%5C%5C%3D%5Cfrac%7B510%7D%7B20%7D%5C%5C%5C%5C%3D25.5%5Capprox%2026)
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](https://tex.z-dn.net/?f=100%5C%25%3D%5Cfrac%7B540%7D%7B0.1%7D%5C%5C%5C%5C%3D%5C%C2%A35400)
#Alternatively, 100% divided by 10% is 10. Multiply this value by £540:
![=540\times 10\\\\=\£5400](https://tex.z-dn.net/?f=%3D540%5Ctimes%2010%5C%5C%5C%5C%3D%5C%C2%A35400)
We subtract the discount amount for the per-discount price:
![Cost=Total -discount\\\\=5400-540\\\\=\£4860](https://tex.z-dn.net/?f=Cost%3DTotal%20-discount%5C%5C%5C%5C%3D5400-540%5C%5C%5C%5C%3D%5C%C2%A34860)
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)](https://tex.z-dn.net/?f=P%28Each%20%5C%20Color%29%3DP%28Yellow%29%3D%5Cfrac%7B1%7D%7B10%7D%5C%5C%5C%5C%5Ctherefore%20P%28Yellow%29%3C0.35%5C%5C%5C%5C0.10%3C0.35)
Hence, this is impossible since 0.10<0.35