Answer:
[tex]13a.\ The \ probability\ of \ scoring\ a\ goal\ in\ a\ game\ is\ 0.36\\\\b. 3 \ games[/tex]
14.
[tex]a. \ \£90\\b. \ 26 \ weeks\\c. \ \£4,860[/tex]
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:
[tex]Games=\frac{1 \ game}{p(goal)}\\\\=\frac{1}{0.36}\\\\=2.778\approx 3[/tex]
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:
[tex]C_g=0.15\times 600\\\\=\£90[/tex]
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:
[tex]t=\frac{Balance}{Rate}\\\\=\frac{600-90}{20}\\\\=\frac{510}{20}\\\\=25.5\approx 26[/tex]
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
[tex]100\%=\frac{540}{0.1}\\\\=\£5400[/tex]
#Alternatively, 100% divided by 10% is 10. Multiply this value by £540:
[tex]=540\times 10\\\\=\£5400[/tex]
We subtract the discount amount for the per-discount price:
[tex]Cost=Total -discount\\\\=5400-540\\\\=\£4860[/tex]
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:
[tex]P(Each \ Color)=P(Yellow)=\frac{1}{10}\\\\\therefore P(Yellow)<0.35\\\\0.10<0.35[/tex]
Hence, this is impossible since 0.10<0.35
