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14.Probability
hard
The probability that a teacher will give an unannounced test during any class meeting is $1/5$. If a student is absent twice, then the probability that the student will miss at least one test is
A
$\frac{4}{5}$
B
$\frac{2}{5}$
C
$\frac{7}{5}$
D
$\frac{9}{{25}}$
Solution
(d) The probability that one test is held $ = 2 \times \frac{1}{5} \times \frac{4}{5} = \frac{8}{{25}}$
Probability that one test is held on both days $ = \frac{1}{5} \times \frac{1}{5} = \frac{1}{{25}}$
Thus the probability that the student misses at least one test $ = \frac{8}{{25}} + \frac{1}{{25}} = \frac{9}{{25}}.$
Standard 11
Mathematics