A person trying to gain access to a bank vault must pass through a series of three security doors. If an attempt to pass through a door is a failure, then the person will not make any further attempts. Let P denote a successful pass and F denote a failed pass. What is the sample space for this random experiment

Sample space is

Step-by-step explanation:

Number of security doors = 3

Let P denote a successful pass and F denote a failed pass.

Sample space refers to a set of all possible outcomes.

If the first attempt to pass through a door is a failure, then the outcome is F.

If the second attempt to pass through a door is a failure, then the outcome is PF.

If the third attempt to pass through a door is a failure, then the outcome is PPF.

If the fourth attempt to pass through a door is a failure, then the outcome is PPP.

Sample space is

C) S = {F, PF, PPF, PPP}

Step-by-step explanation:

For this case, we know that a person is trying to gain access to a bank vault and needs to go through 3 security doors, and we know that if the person does not pass a door, then he/she has no other attempts. We denote P= Successful pass , F= Failed pass

And we are interested on the sample space, we need to remember that the sample is the set with all the possible values for an experiment.

For this case the person can fail at the 1,2 or 3 try

For the case that fails at the 1 try we have F

For the case that fails at the 2 try we have PF

For the case that fails at the 3 try we have PPF

And the last option is that the person not fails at any try and we have PPP

So then the sample space would be given by:

C) S = {F, PF, PPF, PPP}

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

The answer is in the image 

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

The answer is in the image 

Speed=Distance/time

Here,

distance=15m

time=1sec

speed=15/1=15m/sec

Distance=Speed*time

time=15min=15*60sec=900sec

Distance travelled in 15 min=15*900=13,500m

=13500/1000 km=13.5Km

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

Given height of gymnasium is 5/6 height of 30 foot ball

therefore height of gymnasium=5/6 * 30

=25 feet