Statistics Problem

Question

1) A survey from the Department of Motor Vehicles was given to local residents in the city of Slothville. The results showed that 60% held a valid driver's license. Of the individuals who held a valid driver's license, 30% had at least one traffic violation whereas 20% who did not have a valid driver's license had at least one traffic violation. What is the probability that an individual does NOT have a traffic violation?

 

2) Assume you are working with a standard deck of 52 cards. There are 13 cards (2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, and ace) in each of four suits (clubs, diamonds, hearts, and spades).

What is P(Ace ∪ Heart) if you draw one card?

 

 

Answer 1

1) 60% have a valid license, so 40% do not have a valid license

of the 60% with a valid license, 70% had no violations (100%-30%=70%)

70%*60%=0.7*0.6=0.42=42% had  no violations

of the 40% that had no valid license, 80% had no violations (100%-20%=80%)

80%*40%=0.8*0.4=0.32=32% had no violations

42%+32%=74% with no violations

 

2)what is the probability of drawing an ace or a heart

there are 4 aces and 13 hearts but one heart is an ace so you can't use the ace of hearts twice

P=(4+12)/52=16/52=4/13 or

P=(3+13)/52=16/52=4/13, or

P=(4/52)+(13/52)-(1/52)=(4+13-1)/52=16/52=4/13