Originally, the box contained twenty-five marbles, ten of which were red, so the probability of drawing a red marble was 

After adding fifteen red marbles, the box contains forty marbles, twenty-five of which are red, so the probability of drawing a red marble is now 

The increase in probability is 

Before removing the twos, there were fifty-two cards, thirteen of which are hearts, making the probability that a randomly-drawn card would be a heart

After removing the twos, there are forty-eight cards, twelve of which are hearts (one heart, the three of hearts, was removed), making the probability that a randomly-drawn card will be a heart

The probability did not change.

We need only compare numbers of cards.

Since no clubs were removed, there are thirteen clubs in the modified deck.

Since one 2, one 3, and one 4 were removed, there are three of each, or nine of these cards total, in the modified deck.

The probability of drawing a club, (A), is greater.

We need only compare numbers of cards.

Since one diamond (the ace of diamonds) was removed, there are twelve diamonds in the modified deck.

Since no jacks, queens, or kings were removed, all four of each (twelve cards total) remain.

This makes the two quantities and, subsequently, the two probabilities, equal.

Box #1 contains  blue marbles out of 30 total. 

Box #2 contains  blue marbles out of 30 total. 

The probability of drawing a blue marble out of Box #1 is the same as that of drawing a blue marble out of Box #2: .

Both modified decks still have four sevens, and both modified decks have forty-eight cards. Therefore, the probability of drawing a seven from the red deck is the same as the probability of drawing a seven from the purple deck: .

The modified deck has had one card of each suit (including one club) removed from the deck, but has been replaced by four cards whose suits we do not know. There are anywhere from twelve to sixteen clubs in this modifiied deck, but without knowing exactly how many, we cannot answer this question.

Billy has a bag of marbles with 5 red marbles, 6 green marbles and 7 blue marbles. What is the probability that Billy will choose a green marble when he reaches into the bag? 

In order to find the probability of anything we must divide the part by the whole. 

We know that the part in this case are the green marbles; there are 6 of them. 

To find the whole, we must add all the parts: 

We then reduce the fraction to get the final answer. 

Rosemary has a bag of marbles with 5 red marbles, 6 green marbles and 7 blue marbles. What is the probability that Rosemary will choose a blue marble when she reaches into the bag? 

In order to find the probability of anything we must divide the part by the whole. 

We know that the part in this case are the blue marbles; there are 7 of them. 

To find the whole, we must add all the parts: 

Removing the jacks from Deck A and putting them into Deck B transfers one spade and three other cards. The result is that:

12 out of 48 cards in Deck A will be spades - this is  of the cards; and,

14 out of 56 cards in Deck B will be spades - this is  of the cards.

This makes the probability of drawing a spade at random the same for both decks.