Question

Sarawong is carrying six pages of math homework and four pages of english homework. a gust of wind blows the pages out of his hands and he is only able to recover seven random pages. what is the probability that he recovers at least five pages of his math homework

Answer 1

The sample space of the experiment (i.e. the total number of ways he can pick 7 random pages out of a total of 6 + 4 = 10 pages) is given by:

$^{10}C_7=120$

If he picks at least 5 pages of maths homework, this means that he either picked 5 pages or 6 pages of maths homework.

The number of ways he can pick 5 or 6 maths homework is given by:

$^6C_5+{ ^6C_6}=6\times1=6$

Therefore, the probability that he recovers at least 5 pages of his math homework is given by:

$\frac{6}{120} = \frac{1}{20}$