It is estimated that only 68% of drivers wear their safety belt. Part A: What is the probability that exactly 3 drivers are wearing their safety belts if a police officer pulls over five drivers? (5 points) Part B: What is the probability the next driver wearing their safety belt that the police officer pulls over is the fifth driver? (5 points) (10 points)

Part A= 32.19%

Part B= 0.713%

Step-by-step explanation:

Part A

There are two possible outcomes here, the driver wears their safety belt (p=0.68) and the driver doesn't wear it (q= 1-0.68= 0.32). The question asking for the probability of exactly 3 drivers using safety belt out of 5 drivers (n=5).  

So, the question asking P(X=3)

The calculation will be:

P(X=x) = nCx ×(p)^x ×(q)^n-x

P(X=3) = 5C3 ×(0.68)^3 ×(0.32)^2

P(X=3) =0.3219= 32.19%

Part B:  

The question implies that the order of driver is important because it said "the fifth driver". If the next driver wearing a safety belt is 5th driver, that means the four drivers before doesn't use it. Then the condition is 4 drivers not using safety belt + 1 driver use the safety belt.  

The probability of the event will be:

p^1 * q^4= 0.68^1 * 0.32^4= 0.00713= 0.713%

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

source

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation: