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The modified deck has had one card of each suit (including one club) removed from the deck, but has been replaced by four cards whose suits we do not know.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.

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

12 out of 49 cards in Deck A will be hearts - this is  of the cards; and,

14 out of 57 cards in Deck B will be hearts - this is  of the cards.

To compare these probabilities, we express them in a common denominator as follows:

Deck A: 

Deck B: 

The probability that a random draw from Deck B will yield a heart is slightly higher.

Catherine has a bag of marbles with 5 red marbles, 6 green marbles and 7 blue marbles. What is the probability that Catherine will choose a red 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 red marbles; there are 5 of them. 

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

The number of balls in the box, in total, will be

 balls,

5 of which will be marked with a "5". 

The probability of drawing a "5" is therefore

The even numbers in the range of 1 to 10 are 2, 4, 6, 8, and 10; the number of balls marked with one of these numbers is 

Similarly, the number of balls marked with one of the odd numbers is

There are more even-numbered balls than odd, so the probability of drawing an even-numbered ball is the greater.

There are   possible rolls of two fair six-sided dice, each of which will come up with equal probability. The set of rolls is shown below, with the ways to roll an even number indicated.

There are 18 ways out of 36 to roll an even sum, making the probability of this event equal to .