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%

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