ระดับความยาก 6.5/10
Ent'42 จากการสำรวจแม่บ้านที่่ชมโทรทัศน์จำนวน 200 คน ปรากฎว่ามี
65 คน ชมละครเรื่องที่ 1
90 คน ชมละครเรื่องที่ 2
45 คน ชมละครเรื่องที่ 2 เรื่องเดียว
35 คน ชมละครเรื่องที่ 3 เรื่องเดียว
15 คน ชมละครเรื่องที่ 1 และเรื่องที่ 3
35 คน ชมละครเรื่องที่ 2 และเรื่องที่ 3
และมี 30 คน ที่ไม่ได้ชมละครทั้ง 3 เรื่องนี้
ถ้าสุ่มเลือกแม่บ้านจากกลุ่มนี้มา 1 คน แล้วข้อใดต่อไปนี้ผิด

1. ความน่าจะเป็นที่จะได้ผู้ที่ดูละครทั้ง 3 เรื่องนี้เท่ากับ 0.05
2. ความน่าจะเป็นที่จะได้ผู้ที่ดูละครอย่างน้่อยหนึ่งเรื่องเท่ากับ 0.85
3. ความน่าจะเป็นที่จะได้ผู้ที่ดูละครเรื่องที่ 1 เรื่องเดียวเท่ากับ 0.2
4. ความน่าจะเป็นที่จะได้ผู้ืั้ดูละครเรื่องที่ 3 เท่ากับ 0.45

เฉลย >> ข้อ 4

ข้อนี้้เป็นโจทย์เรื่องเซตผสมกับความน่าจะเป็นแบบง่ายๆครับ
ก่อนอื่นเลยเมื่อเจอปัญหาเรื่องเซต เราต้องวาดแผนภาพแล้วระบุสิ่งที่เรารู้ก่อนครับ
โดยส่วนมากแล้วตรงที่ intersection กันระหว่าง 3 เซตถ้าเราไม่รู้ข้อมูลของตำแหน่งนี้
เราจะให้เป็น x ไปครับ จะได้แผนภาพดังรูป

ต่อไปเราก็ต้องตั้งสมการเพื่อหาค่า x การตั้งสมการนี้น้องๆจะตั้งอย่างไรก็ได้ให้สอดคล้องกับข้อมูลที่มีอยู่
และมี x เข้ามาเกี่ยวข้องเพื่อที่จะได้ทราบว่าค่า x เป็นเท่าไร
เมื่อเราพิจารณารูปดีแล้วจะได้ดังรูป

ทำให้เราสามารถตั้งสมการได้ว่า 200 = 65+45+(35-x)+35+30 และแก้สมการได้ค่า x = 10

ต่อไปให้เราวาดภาพใหม่ที่ได้จากการแทนค่า x เข้าไปแล้วได้ดังรูป

ุถ้าใครไม่สามารถเติมเลขลงไปในรูปได้ ขอแนะนำให้ไปทบทวนเรื่องเซตใหม่อีกรอบหนึ่งครับ

จากนั้นเราค่อยมาเทียบกับตัวเลือกทั้งสี่ตัวเลือก
1.ความน่าจะเป็นที่จะได้ผู้ที่ดูละครทั้ง 3 เรื่องนี้เท่ากับ จำนวนคนที่ดูละครทั้ง 3 เรื่อง / จำนวนคนทั้งหมด
= 10/200 = 0.05 ดังนั้นข้อนี้ถูก
2.ความน่าจะเป็นที่จะได้ผู้ที่ดูละครอย่างน้่อยหนึ่งเรื่องเท่ากับ จำนวนคนที่ดูละครอย่างน้อย 1 เรื่อง /
จำนวนคนทั้งหมด = (200-30)/200 = 0.85 ดังนั้นข้อนี้ก็ถูกอีกเช่นกัน
3.ความน่าจะเป็นที่จะได้ผู้ที่ดูละครเรื่องที่ 1 เรื่องเดียวเท่ากับ 40 / 200 = 0.05 ดังนั้นข้อนี้กูกครับ
4.ความน่าจะเป็นที่จะได้ผู้ืั้ดูละครเรื่องที่ 3 เท่ากับ (35+5+10+25) / 200 = 0.375 ดังนั้นข้อนี้ผิดครับ

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