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Câu 61 trang 94 SGK Đại số và Giải tích 11 Nâng cao

Chọn ngẫu nhiên một số tự nhiên bé hơn 1000. Tính xác suất để số đó :
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Chọn ngẫu nhiên một số tự nhiên bé hơn 1000. Tính xác suất để số đó :

LG a

Chia hết cho 3

Lời giải chi tiết:

✃Các số chia hết cho 3 có dạng 3k với \(0 \le 3k < 1000 \)

💙\(\Leftrightarrow 0 \le k < 333,3 \)\(\Rightarrow k \in \left\{ {0;1;...;333} \right\}\)

❀Gọi A là biến cố “số chọn ra chia hết cho 3”. Khi đó :

ΩA = {3k|k ∈ N,0 ≤ k ≤ 333}

⇒ |ΩA| = 334

Do đó xác suất để số chia hết cho 3 là: \(P = {{334} \over {1000}} = 0,334.\)

LG b

Chia hết cho 5

Lời giải chi tiết:

Các số chia hết cho 5 có dạng 5k với \(0 \le 5k < 1000 \) \(\Leftrightarrow 0 \le k < 200 \)\(\Rightarrow k \in \left\{ {0;1;...;199} \right\}\) Gọi B là biến cố “số chọn ra chia hết cho 5”. Khi đó :

ΩB = {5k|k ∈ N,0 ≤ k ≤ 199}

⇒ |ΩB| = 200

Do đó \(P = {{200} \over {1000}} = 0,2\)

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