Download Probability Sample Unit With Answers

Probability Mastery Sampler
1. Determine the probability of drawing a red queen from a deck of cards.
2. A bag contains 4 red marbles, 3 blue marbles, 6 black marbles, and 2 yellow marbles. If a marble is
drawn at random, determine the probability of not drawing a red marble.
3. A box contains balls with the numbers 1 to 40 on it. One ball is drawn randomly. The probability of
the event :choosing a number divisible by 3 is to be determined. State the value of
.
4. A spinner is divided into 21 equal sectors, numbered 1 through 21. Determine the probability of
spinning a number other than an even number.
5. Two six-sided dice are rolled. What is the probability of rolling doubles?
6. The letters of the word MISSISSIPPI are put in a hat and one letter is drawn randomly. What is the
probability that the letter S is selected?
7. What is the probability of rolling a sum greater than ten with two six-sided dice?
8. Four coins are tossed up together. Determine the probability that all four tosses are heads.
9. A card is drawn randomly from a regular deck of cards. Determine the probability of choosing a red
face card.
10. According to the Venn diagram, what is the value of P( A  B) ?
11. According to the Venn diagram, state the value of
.
12. If a card is drawn randomly from a regular deck of cards, determine the probability that it is red or a
face card.
13. Two six-sided dice are rolled. Determine the probability of rolling pairs or a sum of four.
14. Statistics show that at a mini-putt course, 40% of customers are male. Of the male customers, 30% are smokers. Of the
female customers, 20% are smokers. If a customer is chosen at random, determine the probability that the customer is a
male non-smoker.
15. Two six-sided dice are rolled. What is the probability that the total will be an odd number given that a
number less than four was rolled on the red die?
16. A card is drawn from a regular deck of cards and replaced. Then a second card is drawn. Determine
the probability that a spade is drawn and then a face card is drawn.
17. A family has four children. Determine the probability that the first and third children are boys.
18. A bag contains 4 chocolate bars and 3 bags of chips. Two items are drawn without replacement.
Determine the probability that exactly one bag of chips is chosen.
19. A six-sided die is rolled and a card is drawn randomly from a regular deck of cards at the same time.
Determine the probability of rolling an even number and drawing a black ace.
20. The letters of the word SIMILE are scrambled. Determine the probability that the word is spelled exactly
backwards
21. Determine the probability of choosing the Jack of Hearts and the King of Clubs out of a regular deck of 52
cards when two cards are randomly chosen without replacement.
22. The starting line up of a co-ed volleyball team must be made up of 3 males and 3 females. If the team has 9
females and 8 males to choose from, determine the probability that Emma, Mary, and Brittany are selected for
the line up.
23. A bag contains six blue marbles, seven red marbles, and four green marbles. If four marbles are drawn
randomly without replacement, determine the probability that three are green.
24. A bag contains 3 green blocks, 5 purple blocks, and 6 red blocks. If four blocks are drawn one at a
time, without replacement, determine the probability that the order is red, red, purple, green.
25. Three cards are drawn from a regular deck, one at a time, without replacement. Determine the probability that
the order is a jack, queen, and then a number 4, 5, or 6.
26. The letters of the word INFINITY are scrambled. Determine the probability that F is the first letter and Y is the
last letter
27. Three die are rolled simultaneously. Determine the probability that a sum of 5 will be rolled.
28. A group of 3 students is chosen randomly from a class of 26 students. Determine the probability that Allison is
one of these students.
29. A committee of 3 students is chosen from 6 music students and 5 drama students. Determine the probability
that exactly 2 are drama students.
Probability Mastery Sampler
Answer Section
1.
p(red queen) =
2.
p(not red) =
3.
Let A be the event of choosing a number divisible by 3, then
is 13
4.
since there are 11 odd numbers and 10 even numbers, p(not even)=
5.
6.
There are 4 S’s out of 11 letters, so p(drawing an S) =
7.
Visualizing the 6 x 6 table of dice, there are 3 possible rolls with a sum greater than 10: 5,6 6,5 and 6,6 Therefore,
8.
Visualizing a tree diagram:
9.
10.
Looking at all outcomes that are part of A OR B (in circle A or B or BOTH)
11.
Looking at the OVERLAP between B and C,
12.
13.
(add outcomes, subtract overlap (2,2))
14.
Visualize the tree diagram,
This is a conditional probability (since smoker and gender are not independent...)
15.
Think about reducing the sample space.... using the grid, we’re only looking at half of it (where one die is < 4)
16.
Events are independent since card is replaced after first draw.
17.
Draw a tree diagram, or think of it as a series of independent events...
18.
Visualize the tree diagram... there are two ways this can happen (two branches of the tree). Multiply along the
branches (AND) and add the probabilities of the two possible outcomes (OR)
19.
20.
21.
Considering two possible orders for this to happen (Jack then King, or King then Jack)
22.
If these three girls are already on the lineup, we must look at the number of lineups that contain these three girls, an any
three boys as a fraction of ALL the possible lineups using any three girls and any three boys.
23.
Consider the number of groups of 4 marbles that have 3 out of the 4 green marbles , then 1 out of the remaining 13 other
marbles This is the numberator (below). The total number of groups is in the denominator --- all possible groups of 4
marbles out of 17.
24.
Multiply the probabilities of each successive outcome....
25.
Multiply succesive outcomes ...
26.
Number of permuations of INFINITy=8!
Number of permutations of 6 middle letters (given F and Y are set)=6!
27.
This can be counted manually, or by visualizing a 3-D table (6x6x6=216 outcomes)
There are 6 possible ways to roll a sum of 5:
113
131
311
122
212
221
So,
28.
The total number of committees of 3 from 26 is:
To figure out the number of committees containing Allison, consider that she is on the commitee, and we must choose 2
out the remaining 25 to put with her. The number of ways this can be done is:
So,
29.