First slide

Theorems of probability

Question

The probability that a teacher will conduct an unannounced test during any class meeting is $\frac{1}{3}$ . If a student of the class is absent thrice, then the probability for the student to miss at least one test is

Moderate

A

$\frac{11}{27}$
B

$\frac{16}{27}$
C

$\frac{19}{27}$
D

$\frac{8}{27}$

Solution

$\begin{matrix} = 1 - t e a c h e r w i l l n o t c o n d u c t a n y t e s t w h e n s t u d e n t w a s a b s e n t \\ = 1 -^{3} C_{0} {(\frac{1}{3})}^{0} {(\frac{2}{3})}^{3} = 1 - \frac{8}{27} = \frac{19}{27} \end{matrix}$

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