In the class of 30 students, seven of them don't have done the homework. The teacher chose randomly 6 students. What is the chance that at least four of them have done their homework?
Answers
0.88 chance that at least four of them have done their homework
Step-by-step explanation:
In the class of 30 students,
7 of them don't have done the homework.
23 of them have done the homework.
The teacher chose randomly 6 students.
6 Students out of 30 can be selected in ³⁰C₆ ways
= 30 * 29 * 28 * 27 * 26 * 25 / 6 * 5 * 4 * 3 * 2 * 1
= 5,93,775
chance that at least four of them have done their homework
= 4 Done home work + 5 Done home work + 6 Done Home Work
= ²³C₄*⁷C₂ + ²³C₅*⁷C₁ + ²³C₆
= 1,85,955 + 2,35,543 + 1,00,947
= 5,22,445
chance that at least four of them have done their homework = 5,22,445 / 5,93,775
= 0.88
0.88 chance that at least four of them have done their homework
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