First slide

Introduction to probability

Question

Seven girls G₁, G₂, G₃, ..., G₇ are such that their ages are in order G₁ < G₂ < G₃ < ….. < G₇. Five girls are selected at random and arranged in increasing order of their ages. The probability that G₅ and G₇ are not consecutive is

Moderate

A

$\frac{20}{21}$
B

$\frac{19}{21}$
C

$\frac{17}{21}$
D

$\frac{13}{21}$

Solution

Required probability = I - P (G₅ and G₇ are consecutive)
$= 1 - \frac{^{4} C_{3}}{^{7} C_{5}} = \frac{17}{21}$

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