Download Homework #1-4: One card is selected at random from a standard

Homework
#1-4: One card is selected at random from a standard deck of playing cards. Determine the
probability of:
P (A or B). Hint use the formula: P(A or B) = P(A) P(B) – P(A and B)
1. A = an ace B = a jack
P(ace) = 4/52 = 1/13
P(jack) = 4/52 = 1/13
P(ace and jack) = 0/52 = 0 as there is no card that is both an ace and a jack
P(ace or jack) = P(ace) + P(jack) – P(ace and jack)
= 1/13 + 1/13 - 0
= 2/13
Answer: 2/13
3. A = an ace
B = a diamond
P(ace) = 4/52
P(diamond) = 13/52
P(ace and diamond) = 1/52 (this is counting the ace of diamonds)
P(ace or diamond) = P(ace) + P(diamond) – P(ace and diamond)
= 4/52 + 13/52 - 1/52
Answer: 16/52 = 4/13
Homework #5-8 use the formula P(A or B) = P(A) + P(B) – P(A and B) to answer the following.
5) If P(A) = 0.5 and P(B) = 0.6 and P(A and B) = 0.2 find P(A or B)
P(A or B) = P(A) + P(B) – P(A and B)
= 0.5 + 0.6 – 0.2
Answer: 0.9
7) If P(A or B) = 0.8, P(A) = 0.5, P(B) = 0.6 find P(A and B)
P(A or B) = P(A) + P(B) – P(A and B)
0.8 = 0.5 + 0.6 – P(A and B)
0.8 = 1.1 – P(A and B)
-1.1__-1.1
-0.3 = -P(A and B)
Answer: P(A and B) = 0.3
Homework: #9 – 12: a single dice is rolled one time. Find the probability of rolling
9) An odd number or a number greater than 2
P(odd number or a number greater than 2) = P(odd) + P(>2) – P(odd and >2)
= 3/6 + 4/6 - 2/6
Answer: 5/6
11) A number less than 3 or greater than 5
P(< 3 or > 5) = P(<3) + P(>5) – P(< 3 and > 5)
= 2/6 + 1/6 - 0/6
Answer: 3/6 = ½
13) A jack or a diamond
P(jack) = 4/52
P(diamond) = 13/52
P(jack and diamond) = 1/52 (this is counting the jack of diamonds)
P(jack or diamond) = P(jack) + P(diamond) – P(jack and diamond)
= 4/52 + 13/52 - 1/52
Answer: 16/52 = 4/13
15) A seven or a six
P(seven) = 4/52 = 1/13
P(six) = 4/52 = 1/13
P(seven and six) = 0/52 = 0 as there is no card that is both a seven and a six
P(seven or six) = P(seven) + P(six) – P(seven and six)
= 1/13 + 1/13 - 0
= 2/13
Answer: 2/13
17) A red card or a ten
P(red) = 26/52
P(ten) = 4/52
P(red and ten) = 2/52 (this is counting the ten of diamonds and hearts)
P(red or ten) = P(red) + P(ten) – P(red or ten)
= 26/52 + 4/52 - 2/52
Answer: 28/52 = 7/13
Homework #19 – 22: One marble is selected from a bag that contains 4 red, 5 white, 6 blue and
2 yellow. Find the probability of selecting
19) A red or a white
P(red or white) = P(red) + P(white) – P(red and white)
4/17 + 5/17
- 0/17
Answer: 9/17
21) A blue or a white
P(blue or white) = P(blue) + P(white) – P(blue and white)
6/17 + 5/17
- 0/17
Answer: 11/17
Homework #23 – 26: The numbers 1, 2, 3, 4, …., 14 are placed on a piece of paper and thrown
into a bucket. One piece of paper is randomly selected. What is the probability that:
23) The number is odd or greater then 7
P(odd or > 7) = P(odd) + P(> 7) – P(odd and > 7)
7/14 + 7/17 - 3/14
Answer: 11/14
25) The number is greater than or equal to 5 or even
Homework #27-30: The letters of the word Mississippi are placed on pieces of paper and
thrown into a bucket. One piece of paper is randomly selected. What is the probability that:
27) The letter is a p or an m?
P(p or m) = P(p) + P(m) – P(p or m)
2/11 + 1/11 – 0-11
Answer: 3/11
29) The letter is a vowel or alphabetically after r?
Hint there are 4 vowels (iiii)
There are 4 letters alphabetically after r (ssss)
There are no letters that are vowels and after r
P(vowel or after r) = P(vowel) + P(after r) – P(vowel and after r)
4/11
+ 4/11
- 0/11
Answer: 8/11