First slide

Random variable and probability distribution

Question

A box contains tickets numbered from 1 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

2/19
B

7/20
C

1 - (7/20)³
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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