First slide

Theorems of probability

Question

A box contains tickets numbered from I to 20. Three tickets are drawn from the box with replacement. The probability that the largest number on the tickets is 7 is

Moderate

A

$\frac{7}{20}$
B

$1 - {(\frac{7}{20})}^{3}$
C

$\frac{2}{19}$
D

None of these

Solution

Let X denote the largest number on the 3 tickets drawn
$Then, P (X \leq 7) = (7 / 20)^{3} and P (X \leq 6) = (6 / 20)^{3} . Then, the required probability is$
$P (X = 7) = {(\frac{7}{20})}^{3} - {(\frac{6}{20})}^{3}$

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