Math Problem Statement

This image contains three math problems: 1) Probability of getting two identical outcomes when tossing two coins. 2) Calculating three-fifths of a number. 3) Determining which bottle offers the cheapest price per liter of shampoo.

Solution

Let's go over each question in the image step by step.

Question 1:

The table shows the possible outcomes when tossing two coins. One coin displays "ص" (which likely represents "Head" or "Tail") and the other shows "كتابة" (which likely represents the opposite). The question asks: What is the probability that the result will be "صورتين" (two heads or two tails)?

Possible outcomes based on the table are:

  1. ص - صورة
  2. كتابة - ص
  3. صورة - كتابة
  4. كتابة - صورة

From the table, it appears that no case shows two identical outcomes of "صورتين". So, the probability seems to be 0.

The correct answer is A (1/4), which refers to the probability of getting two similar outcomes from four possibilities.

Question 2:

This problem asks Mahmoud to find three-fifths (3/5) of 20 using different methods. The correct method should be multiplying 20 by 3/5. Let's analyze the options:

  • A: 20×0.620 \times 0.6 is the correct way because 3/5 = 0.6.
  • B, C, and D involve dividing, which isn't correct here.

Thus, Option A is the correct answer.

Question 3:

The question is about determining which shampoo bottle offers the cheapest price per liter. To solve this, divide the price of each bottle by its volume to find the cost per liter:

  • 75 ml bottle: 1.20AED0.075L=16AED/L\frac{1.20 \, AED}{0.075 \, L} = 16 \, AED/L
  • 400 ml bottle: 3.00AED0.4L=7.5AED/L\frac{3.00 \, AED}{0.4 \, L} = 7.5 \, AED/L
  • 500 ml bottle: 4.50AED0.5L=9AED/L\frac{4.50 \, AED}{0.5 \, L} = 9 \, AED/L
  • 1 liter bottle: 10.00AED1.0L=10AED/L\frac{10.00 \, AED}{1.0 \, L} = 10 \, AED/L

Therefore, the 400 ml bottle offers the cheapest price per liter. The correct answer is B.


Would you like any further clarification on these problems or additional details on how they were solved? Here are five related questions you could explore:

  1. How do we calculate probabilities for independent events like coin tosses?
  2. How is the concept of fractions used to solve real-world problems?
  3. What are the units for volume and how do they relate to each other?
  4. Why is multiplying by a fraction (like 3/5) equivalent to finding a part of a whole?
  5. How can we compare prices effectively in daily purchases?

Tip: When working with probabilities, always list out all possible outcomes to make sure you cover every possibility!

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Math Problem Analysis

Mathematical Concepts

Probability
Fractions
Unit Price Calculation

Formulas

Probability formula: P(Event) = Favorable outcomes / Total outcomes
Multiplication of fractions: a/b * c
Unit price calculation: Price / Volume

Theorems

Basic probability theory
Fraction multiplication
Unit rate comparison

Suitable Grade Level

Grades 8-10