Subjects probability

Navbatda Uchta Odam 8Ad687

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Navbatda Uchta Odam 8Ad687


1. Masala: A va B orasida uchta odam bo'lish ehtimolini topish. 2. Berilgan: A va B navbatda turibdi, ular orasida yana 8 odam bor, jami 10 odam. 3. Masala sharti: A va B orasida aniq 3 odam bo'lishi kerak. 4. Bu kombinatorik masala, ya'ni 8 odam orasidan 3 tasini tanlash ehtimoli: $$ P = \frac{\binom{8}{3}}{\binom{10}{3}} $$ 5. Hisoblaymiz: $$ \binom{8}{3} = \frac{8!}{3!5!} = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = 56 $$ $$ \binom{10}{3} = \frac{10!}{3!7!} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120 $$ 6. Shunday qilib, ehtimol: $$ P = \frac{56}{120} = \frac{7}{15} \approx 0.4667 $$ Javob: A va B orasida uchta odam bo'lish ehtimoli $\frac{7}{15}$ yoki taxminan 0.467.