Math Problem Statement

The query involves probability, fractions, and unit rates based on three different questions presented in a math exam format. The questions require calculating probabilities for a two-coin flip, finding a fraction of a number, and determining the cheapest price per liter for a product.

Solution

Let's break down the questions shown in the image:

Question 1:

It involves two coins, each with two possible outcomes: "صورة" (Heads) and "كتابة" (Tails). The table provides the results of flipping both coins.

The question asks for the probability of getting "صورة" (Heads) on both flips. There are 4 possible outcomes (two for each coin):

  • صورة - صورة
  • صورة - كتابة
  • كتابة - صورة
  • كتابة - كتابة

Only one of these outcomes is "صورة - صورة". Therefore, the probability is 14\frac{1}{4}.
Answer: A

Question 2:

The task is to find three-fifths of 20 using equivalent fractions. The calculation 35×20\frac{3}{5} \times 20 should be performed. We can either:

  • Multiply 20×3=6020 \times 3 = 60, and then divide by 5, giving 605=12\frac{60}{5} = 12.

So the answer is 12, which corresponds to option C.

Answer: C

Question 3:

The question asks which bottle offers the cheapest shampoo per liter. To solve this, we need to find the price per liter for each bottle:

  • 75 ml costs AED 1.20 → 1.200.075\frac{1.20}{0.075} = 16 AED/liter
  • 400 ml costs AED 3.00 → 3.000.400\frac{3.00}{0.400} = 7.5 AED/liter
  • 500 ml costs AED 4.50 → 4.500.500\frac{4.50}{0.500} = 9 AED/liter
  • 1 liter costs AED 10.00 → 10 AED/liter

Thus, the 400 ml bottle provides the lowest cost per liter (7.5 AED/liter). Answer: B

Would you like further details or clarification on any part? Here are five related questions to explore:

  1. What is the probability of flipping two tails in a two-coin toss?
  2. How can you apply probability theory to larger sets of possible outcomes?
  3. What are the steps to solve equivalent fractions in different scenarios?
  4. How do unit rates help in comparing prices in real-life scenarios?
  5. What is the significance of simplifying fractions when dealing with word problems?

Tip: When calculating probabilities, ensure that all possible outcomes are considered equally likely, unless otherwise stated.

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Math Problem Analysis

Mathematical Concepts

Probability
Fractions
Unit Rates

Formulas

Probability formula: P(Event) = Number of favorable outcomes / Total number of outcomes
Fraction multiplication: a/b * c = (a * c)/b
Unit rate: Price per liter = Price / Volume

Theorems

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Suitable Grade Level

Grade 5-6