In: Math
In a town, 36% of the citizens contributed to the Republicans, 46% contributed to the Democrats, and 12% contributed to both. What percentage contributed to neither party?
A box contains 4 white, 3 red, and 3 black marbles. One marble is chosen at random, and it is not black. Find the probability that it is white. (Enter your answer as a fraction.)
Suppose that 90% of drivers are "careful" and 10% are
"reckless." Suppose further that a careful driver has a 0.2
probability of being in an accident in a given year, while for a
reckless driver the probability is 0.3. What is the probability
that a randomly selected driver will have an accident within a
year? (Enter your answer to two decimal places.)
1 . In a Town :
Percentage citizens who contributed to neither party = P ( R ' D ' )
By Axiom of Probability , we know that :
P ( R D ) = P ( R ) + P ( D ) - P ( R D ) = 0.36 + 0.46 - 0.12 = 0.70
P ( R ' D ' ) = P ( R D ) ' = 1 - P ( R D ) = 1 - 0.70 = 0.30 = 30 %
2 . A Box Contains 10 Marbles of which :
A Marble is chosen at random and it is not black . Thus , our Sample space cuts down to 7 Marbles of which 4 are White and 3 are Red .
P ( Chosen Marble is White ) = 4 / 7
3 . Given that :
We use Law of Total Probability which states that :
P ( X ) = P ( X | Y i ) * P ( Y i )
P ( Randomly Selected Driver will have Accident within a year )
P ( A ) = [ P ( A | C ) * P ( C ) ] + [ P ( A | R ) * P ( R ) ]
= 0.2 ( 0.9 ) + 0.3 ( 0.1 ) = 0.18 + 0.03 = 0.21