The probability that three men hit a target are respectively 1.docx
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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
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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