Statistics · 3rd secondary · First Term

Probability — Conditional probability

About this lesson

This unit covers probability concepts, starting with mutually exclusive events and events that are not mutually exclusive, including their formulas for union and complement. It then introduces conditional probability, defined as P(A|B) = P(A∩B)/P(B) for P(B)>0, and explains how the occurrence of one event can affect the probability of another. The unit includes worked examples using dice rolls, balls drawn from a bag without replacement, tables of data (e.g., glasses-wearing, language study, sports teams, votes), and Venn diagrams. Students learn to compute conditional probabilities, use the multiplication rule P(A∩B)=P(A|B)P(B), and apply these to real-world contexts. By the end, students should be able to calculate conditional probabilities from given data or scenarios, use tree diagrams for sequential events, and solve problems involving conditional probability.

Main topics in this lesson

  • Mutually exclusive events
  • Events not mutually exclusive
  • Conditional probability definition and formula
  • Applications with dice, balls, tables, and Venn diagrams
  • Tree diagrams for sequential events

Key terms and vocabulary

  • Mutually exclusive events
  • Events are not mutually exclusive
  • Conditional probability
  • Sample space
  • Event
  • Intersection
  • Union
  • Complement
  • Tree diagram
  • Venn diagram

Questions and answers on Probability — Conditional probability - practice and revision

Multiple choice questions on this lesson in Statistics for 3rd secondary, First Term, with practice exercises for revision and exam preparation.

1

إذا كان P(A|B) = 0.5 و P(A∩B) = 0.15، فما قيمة P(B)؟

  • 1 0.3
  • 2 0.075
  • 3 0.65
  • 4 0.35
2

في تجربة رمي حجر نرد منتظم مرتين، ما احتمال الحصول على 6 في الرمية الثانية علماً بأن الرمية الأولى كانت 6؟

  • 1 1/6
  • 2 1/36
  • 3 1/3
  • 4 1/2
3

في جدول يوضح 50 شخصاً، 30 منهم يلبسون نظارة و 20 لا يلبسونها، ومن بين لابسي النظارة 12 أنثى. إذا اختيرت أنثى عشوائياً، فما احتمال أنها تلبس نظارة؟

  • 1 لا يمكن تحديدها من البيانات المعطاة
  • 2 12/30
  • 3 12/50
  • 4 30/50
4

إذا كان A و B حدثين غير متنافيين حيث P(A) = 0.5 و P(B) = 0.4 و P(A∩B) = 0.2، فما قيمة P(A∪B)؟

  • 1 0.7
  • 2 0.9
  • 3 0.2
  • 4 1.1
5

إذا كان P(A∩B) = 0.2 و P(A) = 0.5، فما قيمة P(B|A)؟

  • 1 0.4
  • 2 0.1
  • 3 0.7
  • 4 2.5
6

في كيس به 4 كرات بيضاء و 6 كرات سوداء، سُحبت كرة بيضاء دون إرجاع، فما احتمال أن تكون الكرة الثانية المسحوبة سوداء؟

  • 1 6/9
  • 2 6/10
  • 3 4/9
  • 4 4/10

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