Question

A real estate man has eight master keys to open several new homes. Only one master key will open any given home. If 40% of these homes are usually left unlocked, the probability that the real estate man can get into a specific home, if it is given that he selected 3 keys randomly before leaving his office, is equal to:

• A. $\frac{5}{8}$
• B. $\frac{3}{8}$
• C. $\frac{3}{4}$
• D. $\frac{9}{40}$

Answer 1

The correct option is A $\frac{5}{8}$

P(he can get into the specific home if specific home is unlocked)
$=\frac{40}{100}\times 1=\frac{2}{5}$
P(he can get into the specific home if specific home is locked)
$=\frac{60}{100}\times \frac{{}^7{C}_2}{{}^8{C}_3}=\frac{3}{5}\times \frac{21}{56}=\frac{9}{40}.$
$\therefore$ Required probability=total probability=$\frac{2}{5}+\frac{9}{40}=\frac{5}{8}$