Data from the Federal Bureau of Investigation show that 1 of

Data from the Federal Bureau of Investigation show that 1 of every 184 motor vehicles was stolen during 2003. Applying this statistics to 5 motor vehicles randomly selected from the nation\'s vehicle population: 1. What is the probability that none of the 5 motor vehicles will be stolen? 2. What is he probability that all 5 motor vehicles will be stolen?3. How many probabilities exist in which 2 of the 5 motor vehicles are stolen?

Solution

Prob for being stolen = 1/184 = 0.00543

Sample size selected = 5

X - no of vehicles being stolen is binomial with p = 0.00543

1) the probability that none of the 5 motor vehicles will be stolen

= 5C0(0.99457)⁵

= 0.9731

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2) probability that all 5 motor vehicles will be stolen

= P(X=5)

= 5C5(0.00543)⁵

= 4.721x10^-12

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3) probabilities exist in which 2 of the 5 motor vehicles are stolen

= P(X=2)

= 5C2(0.00543)²(0.99457)³

= 0.00029