Question

There are 10 vehicles in a parking lot: 3 SUVs and 7 trucks.
What is the probability that of any 7 randomly chosen vehicles, exactly 1 is an SUV?

Answer 1

S=SUV
T=truck
7 possible outcomes for exactly 1 SUV
STTTTTT
TSTTTTT
TTSTTTT
TTTSTTT
TTTTSTT
TTTTTST
TTTTTTS
Each of these outcomes has a probability of
\[\frac{3}{10}\frac{7}{9}\frac{6}{8}\frac{5}{7}\frac{4}{6}\frac{3}{5}\frac{2}{4}=\frac{1}{10}\]
So with all 7 possible outcomes,
probability = 7/10

Answer 2

Can someone please explain how to find the possible outcome f having 7 vehicles in a parking lot.

Answer 3

@melisamangeee
@anjelina24dtl
On second thought, I would do it differently using multinomial arrangements.
X=Number of ways of arranging 7 vehicles, out of which 1 is an SUV
= 7!/(6!1!)
=7
N=Number of ways of arranging 10 vehicles, 3 of which are SUV's
=10!/(7!3!)
=120

Probability of choosing 1 SUV among 7 total vehicles out of 7 trucks and 3 SUV's
= 7/120