Download 1.) A card is selected from a standard deck of 52

1.) A card is selected from a standard deck of 52 playing cards. A standard deck of cards
has 12 face cards and four Aces (Aces are not face cards). Find the probability of
selecting
· a three given the card is a not a face card.
Given that the card is not a face card, there are 40 non-face cards and 4 threes.
The probability that the card is a three is 4/40 = 1/10 = 0.10
· a four, given that the card is not a diamond.
Given that the card is not a diamond, there are 39 non-diamond cards.
There are only 3 fours remaining, since the 4 of diamonds is excluded.
The probability that the card is a four is 3/39 = 1/13
· a Jack given the card is not a face card.
Since it is given that the card is not a face card, and since a Jack IS a face card,
the probability that the card is Jack is 0.
Show step by step work. Give all solutions exactly in reduced fraction form.
2.) A mini license plate for a toy car must consist of three numbers followed by a letter.
Each number must be a 1, 3, or 5. Repetition of digits is NOT permitted. Each letter must
be an A, B or C.
*Use the counting principle to determine the number of points in the sample space.
There are 3 choices for the first number, 2 choices for the second number, 1
choice for the third number, and three choices for the letter.
The total number of combinations is then:
3 * 2 * 1 * 3 = 18
*Construct a tree diagram to represent this situation
*List the sample space.
135A
135B
135C
153A
153B
153C
315A
315B
315C
351A
351B
351C
513A
513B
513C
531A
531B
531C
*Determine the exact probability of creating a mini license plate with a C. Give solution
exactly in reduced fraction form.
There are 6 plates that contain a C, and a total of 18 plates.
The probability of a plate having a C is 6/18 = 1/3
3.) A bag contains 6 purple marbles, 7 azure marbles and 10 orange marbles. What is the
chance of drawing an orange marble? If an orange marble is drawn then placed back into
the bag, and a second marble is drawn, what is the probability of drawing an azure
marble? Give solutions exactly in reduced fraction form, separated by a comma.
There are a total of 6 + 7 + 10 = 23 marbles.
The probability of drawing an orange marble is 10/23.
The probability of drawing an azure marble is 7/23.