If you pick a card at random from a well shuffled deck, what is the probability that you get a face card or a spade?
a) 3/26 is that correct
In one town, 336% of all voters are Democrats. If two voters are randomly selected for a survey find the probability that they are both Democrats.
c) 0.690
a) No. There are 12 face cards (4 x 3) and 10 spades that are not face cards . The probability you get one or the other is 22/52.
b) How can 336% of voters be Democrats? Do you mean 33.6%? If so, the answer is (0.336)^2
If the number of voters is very large, the probability of getting the same party twice in a row is the square of whatever the probability is for a single selection.
a) The correct probability of getting a face card or a spade from a well-shuffled deck is (12 + 13 - 3)/52. There are 12 face cards (3 suits with 4 each), 13 spades (including the 3 face cards), and we subtract 3 because the 3 face cards (jack, queen, king) are already counted in both categories. So the probability is (12 + 13 - 3)/52 = 22/52 = 11/26.
b) If 33.6% of voters in a town are Democrats, the probability that two randomly selected voters are both Democrats can be calculated by multiplying the probability of one voter being a Democrat by the probability of the second voter also being a Democrat. So the probability is (0.336) * (0.336) = 0.112896, which is approximately 0.113 or 11.3%.