Girls only

Probability Level pending

Thirty boys and forty girls are in a room. A team of 3 persons is formed such that it is composed of a team leader, a secretary and a bodyguard. What is the probability that a team formed is composed of a girl secretary?

\frac{5}{7}

\frac{870}{2737}

\frac{4}{7}

\frac{290}{2737}

1 solution

A Former Brilliant Member
Jan 11, 2017

number of boys = $30$

number of girls = $40$

total = $70$

Consider the girls only.

$P=$ $\frac{40}{70}=$ $\boxed{\frac{4}{7}}$

Alternate solution:

We consider the order: leader, secretary, bodyguard

B=boy; G=girl

$BBB$

$BBG$

$BGB =$ $(\frac{30}{70})$ $(\frac{40}{69})$ $(\frac{29}{68})=$ $\frac{290}{2737}$

$GBB$

$GGB =$ $(\frac{40}{70})$ $(\frac{39}{69}$ $(\frac{30}{68}) =$ $\frac{390}{2737}$

$GBG$

$BGG =$ $(\frac{30}{70})$ $(\frac{40}{69})$ $(\frac{39}{68}) =$ $\frac{390}{2737}$

$GGG =$ $(\frac{40}{70})$ $(\frac{39}{69})$ $(\frac{38}{68}) =$ $\frac{494}{2737}$

$P=$ $\frac{290}{2737}$ $+$ $\frac{390}{2737}$ $+$ $\frac{390}{2737}$ $+$ $\frac{494}{2737}=$ $\boxed{\frac{4}{7}}$

Girls only

1 solution

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