A 3 or less can be rolled the following ways:

Both dice can be 1, for a roll of 2. This can happen  ways, since each die has three 3's.

The first die can be 1 and the second die can be 2, for a roll of 3. This can happen  ways, as each die has three 3's and two 2's.

Similarly, the first die can be 2 and the second die can be 3 - by symmetry, this can happen 6 ways.

This is  outcomes out of 36 rolls that are favorable to the event, leaving  unfavorable outcomes. This makes (a) greater.

Since the population increased over both the first and second half-decade, the population in 1965 had to be between the 1960 and 1970 levels - that is, it was between 3,415 and 3,866.

Therefore (b) is greater.

Four cards, including one spade (the ace of spades) changed decks.

Deck 1 now has forty-eight cards, including twelve spades. Therefore,  of its cards are spades.

Deck 2 now has fifty-six cards, including fourteen spades. Therefore,  of its cards are spades.

Therefore, the probability that a random card from either deck will be a spade is  for both decks.

There are four kings and two red threes, making six favorable outcomes and forty-six unfavorable ones. The odds against a favorable outcome are

or 23 to 3.

Out of fifty-two cards, the winning cards are the thirteen spades and the three other aces - sixteen winning cards and thirty-six losing cards. The odds against drawing a winning card are therefore

or 9 to 4.

The two jokers bring the deck to fifty-four cards; since there are four aces, four kings, and two jokers, there are ten favorable outcomes and forty-four unfavorable outcomes. This makes the odds against a favorable outcome

or 22 to 5.

One thirteenth of 52 is 

so we are looking for an outcome that has four simple events - that is, four cards.

Drawing an Old Maid card: since a standard deck definitely does not have an Old maid card, this is incorrect.

Drawing a black three: there are two black threes, so this is not correct.

Drawing a red face card (king, queen, jack): This outcome includes two kings, two queens, and two jacks - six cards. This is not correct.

Drawing a heart: There are thirteen hearts, so this is not correct.

Drawing a black four or a black five: There are two black fours and two black fives - four cards. This is the correct response.

The modified deck will have 78 cards (the original 52 plus the added 26), 26 of which will be spades (the original 13 plus the added 13). The probability of drawing a spade will therefore be 

The modified deck will have 78 cards (the original 52 plus the added 26), 6 of which are aces (the original 4 plus the added ace of diamonds and ace of clubs); the probability that an ace will be drawn is

The quantities are equal.

After the four kings - one of which is a spade - are transferred between decks, Deck 2 has fourteen spades out of fifty-six cards overall. This makes the probability of drawing a spade

.

This is not among the given choices, so the correct response is "none of these".