The probability that three men hit a target are respectively 1.docx
•Download as DOCX, PDF•
1 like•298 views
The probability that three men hit a target are respectively 1/6, ¼ and 1/3. Each shoots once at the target. If only one hit the target, What is the probability that it was the first man
Recommended
Recommended
More Related Content
What's hot
What's hot (20)
More from Nadeem Uddin
More from Nadeem Uddin (20)
Recently uploaded
Recently uploaded (20)
The probability that three men hit a target are respectively 1.docx
- 1. The probability that three men hit a target are respectively 1/6, ¼ and 1/3. Each shoots once at the target. If only one hit the target, What is the probability that it was the first man? Solution 𝑴 = 𝑯𝒊𝒕 𝒕𝒉𝒆 𝒕𝒂𝒓𝒈𝒆𝒕 𝑴 ̅ = 𝑵𝒐𝒕 𝒉𝒊𝒕 𝒕𝒉𝒆 𝒕𝒂𝒓𝒈𝒆𝒕 𝑷(𝑴𝟏) = 𝟏 𝟔 𝑷(𝑴 ̅ 𝟏) = 𝟓 𝟔 𝑷(𝑴𝟐) = 𝟏 𝟒 𝑷(𝑴 ̅ 𝟐) = 𝟑 𝟒 𝑷(𝑴𝟑) = 𝟏 𝟑 𝑷(𝑴 ̅ 𝟑) = 𝟐 𝟑 𝑷(𝑶𝒏𝒍𝒚 𝒐𝒏𝒆 𝒎𝒂𝒏 𝒉𝒊𝒕 𝒕𝒉𝒆 𝒕𝒂𝒓𝒈𝒆𝒕) = 𝑷(𝑯) 𝑷(𝑯) = 𝑷(𝑴𝟏) × 𝑷(𝑴 ̅ 𝟐) × 𝑷(𝑴 ̅ 𝟑) + 𝑷(𝑴 ̅ 𝟏) × 𝑷(𝑴𝟐) × 𝑷(𝑴 ̅ 𝟑) + 𝑷(𝑴 ̅ 𝟏) × 𝑷(𝑴 ̅ 𝟐) × 𝑷(𝑴𝟑) 𝑷(𝑯) = 𝟏 𝟔 × 𝟑 𝟒 × 𝟐 𝟑 + 𝟓 𝟔 × 𝟏 𝟒 × 𝟐 𝟑 + 𝟓 𝟔 × 𝟑 𝟒 × 𝟏 𝟑
- 2. 𝑷(𝑯) = 𝟔 + 𝟏𝟎 + 𝟏𝟓 𝟕𝟐 = 𝟑𝟏 𝟕𝟐 𝑷(𝑭𝒊𝒓𝒔𝒕 𝒎𝒂𝒏 𝒉𝒊𝒕 𝒕𝒉𝒆 𝑯 ⁄ ) = 𝑷(𝑭 𝑯 ⁄ ) 𝑷(𝑭 𝑯 ⁄ ) = 𝑷(𝑴𝟏) × 𝑷(𝑴 ̅ 𝟐) × 𝑷(𝑴 ̅ 𝟑) 𝑷(𝑯) 𝑷(𝑭 𝑯 ⁄ ) = 𝟏 𝟔 × 𝟑 𝟒 × 𝟐 𝟑 𝟑𝟏 𝟕𝟐 = 𝟔 𝟑𝟏