Ratios, Percentages, Probability & Inference

Practice Questions

Level 1: Easy (Foundational)

1. A recipe uses flour and sugar in the ratio $5:3$. If $200$ g of flour is used, determine the exact grams of sugar required. (SPR)
2. What is $15\%$ of $240$?
   A) $24$
   B) $30$
   C) $36$
   D) $45$
3. A fair coin is tossed twice. What is the exact probability of exactly one head?
   A) $\tfrac{1}{4}$
   B) $\tfrac{1}{2}$
   C) $\tfrac{3}{4}$
   D) $1$

Level 2: Medium (Standard)

1. A price is discounted $20\%$ from $\$50$, then reduced a further $10\%$. Determine the exact final price in dollars.
   A) $\$34$
   B) $\$36$
   C) $\$38$
   D) $\$40$
2. The mean of $5$ integers is $12$. When a $6^{\text{th}}$ integer is added the mean becomes $14$. Determine the exact value of the added integer.
   A) $14$
   B) $18$
   C) $20$
   D) $24$
3. A bag contains $3$ red, $2$ green, $5$ blue marbles. Determine the exact probability, as a decimal, of drawing a red marble. (SPR)
4. Events $A$ and $B$ are independent with $P(A)=0.4$ and $P(B)=0.5$. Determine $P(A \cap B)$.
   A) $0.1$
   B) $0.2$
   C) $0.4$
   D) $0.9$

Level 3: Hard (Advanced)

1. In a survey, $70\%$ of students study daily; among daily studiers, $80\%$ score $\ge 7$. What is the probability a random student studies daily AND scores $\ge 7$?
   A) $0.14$
   B) $0.36$
   C) $0.50$
   D) $0.56$
2. A dataset has mean $50$ and standard deviation $8$. By the empirical rule, approximately what percent of values fall in $[42, 58]$?
   A) $50\%$
   B) $68\%$
   C) $95\%$
   D) $99.7\%$
3. A $95\%$ confidence interval for a mean is $(48, 52)$. Determine the exact value of the sample mean $\bar{x}$. (SPR)