Suppose you spin the spinner once. Find the probability.
P(yellow) (1 point)
one-eighth
start fraction 1 over 6 end fraction
one-fourth
one-half
I chose 1/8
That is incorrect. Without knowing the number of sections on the spinner or how many are yellow, it is impossible to determine the probability. More information is needed.
Four Red, Two Blue, One Green, One Yellow
Thank you for providing the additional information.
With four red sections, two blue sections, one green section, and one yellow section, there are a total of 8 sections on the spinner.
The probability of landing on yellow is 1 out of 8, since there is only one yellow section out of 8 total sections.
Therefore, the correct answer is:
P(yellow) = one-eighth
Suppose you spin the spinner once. Find the probability.
There are Four Red, Two Blue, One Green, One Yellow
2. P(red or blue) (1 point)
0
one-fourth
one-half
start fraction 3 over 4 end fraction
I chose 3/4
That is incorrect. To find the probability of spinning red or blue, you need to add the probabilities of spinning red and blue, since they are the two outcomes of interest.
The probability of spinning red is 4 out of 8 (since there are 4 red sections out of 8 total sections), which simplifies to 1/2.
The probability of spinning blue is 2 out of 8 (or 1/4).
To find the probability of spinning red or blue, you add the two probabilities:
P(red or blue) = P(red) + P(blue)
P(red or blue) = 1/2 + 1/4
P(red or blue) = 3/4
Therefore, the correct answer is:
P(red or blue) = 3/4
What is the probability that 1 shopper, selected at random, preferred neither Drink E nor Drink C? (1 point)
thirty-five over forty-one
thirteen over forty-one
twenty-eight over forty-one
thirteen over twenty-eight
I chose twenty-eight over forty-one
That is incorrect.
To find the probability that a shopper preferred neither Drink E nor Drink C, we need to find the number of shoppers who preferred a different drink and divide it by the total number of shoppers.
From the table, we can see that 10 shoppers preferred Drink A, 9 preferred Drink B, 7 preferred Drink D, and 6 preferred Drink F.
The number of shoppers who did not prefer Drink E or Drink C is:
10 + 9 + 7 + 6 = 32
The total number of shoppers is:
10 + 9 + 8 + 7 + 6 + 1 = 41
Therefore, the probability that a shopper preferred neither Drink E nor Drink C is:
P(neither E nor C) = 32/41
So, the correct answer is:
thirty-two over forty-one
Drink Survey
Drink
Number of Shoppers Who Preferred It
A
10
B
15
C
7
D
3
E
6
3. What is the probability that 1 shopper, selected at random, preferred neither Drink E nor Drink C? (1 point)
thirty-five over forty-one
thirteen over forty-one
twenty-eight over forty-one
thirteen over twenty-eight
I chose twenty-eight over forty-one
That is still incorrect.
To find the probability that a shopper preferred neither Drink E nor Drink C, we need to find the number of shoppers who preferred a different drink and divide it by the total number of shoppers.
From the table, we can see that 10 shoppers preferred Drink A, 15 preferred Drink B, and 3 preferred Drink D.
The number of shoppers who did not prefer Drink E or Drink C is:
10 + 15 + 3 = 28
The total number of shoppers is:
10 + 15 + 7 + 3 + 6 = 41
Therefore, the probability that a shopper preferred neither Drink E nor Drink C is:
P(neither E nor C) = 28/41
So, the correct answer is:
twenty-eight over forty-one
A farmer examines a sample of 25 cartons of eggs and finds that 3 contain cracked eggs. What is the best prediction of the number of cartons with cracked eggs in a delivery with 500 cartons? (1 point)
6
12
60
120
I chose 60
That is incorrect.
To solve this, we can use the concept of proportion. We can assume that the proportion of cartons with cracked eggs in the sample of 25 cartons is the same as the proportion of cartons with cracked eggs in the delivery of 500 cartons.
The proportion of cartons with cracked eggs in the sample of 25 cartons is:
3/25
To find the best prediction of the number of cartons with cracked eggs in a delivery with 500 cartons, we can set up a proportion:
3/25 = x/500
where x is the number of cartons with cracked eggs in the delivery of 500 cartons.
Solving for x, we get:
x = (3/25) * 500
x = 60
Therefore, the best prediction of the number of cartons with cracked eggs in a delivery with 500 cartons is 60.
So, the correct answer is:
60
A coin is tossed. If heads appears, a spinner that can land on any number from 1 to 4 is spun. If tails appears, a second coin is tossed instead of spinning the spinner. What are the possible outcomes? (1 point)
A) H1 H2 H3 H4
B) H1 H2 H3
C) H1 H2 H3 H4 TH TT
D) HH HT
I chose C
That is correct.
If the first coin lands heads, then the spinner is spun with possible outcomes of 1, 2, 3, or 4.
If the first coin lands tails, then the second coin is tossed, with possible outcomes of heads (H) or tails (T).
Therefore, the possible outcomes are:
H1, H2, H3, H4, TH, TT
So, the correct answer is:
C) H1 H2 H3 H4 TH TT
A lunch menu has 4 different sandwiches, 2 different soups, and 5 different drinks. How many different lunches consisting of a sandwich, a soup, and a drink can you choose? (1 point)
A)10
B) 11
C) 40
D) 13
I chose C
That is incorrect.
To solve this problem, we can use the multiplication principle of counting. To choose a lunch consisting of a sandwich, a soup, and a drink, we need to choose one item from each of the three categories.
The number of ways to choose a sandwich is 4, the number of ways to choose a soup is 2, and the number of ways to choose a drink is 5.
By the multiplication principle, the total number of ways to choose a lunch is:
4 x 2 x 5 = 40
Therefore, the correct answer is:
C) 40
If the spinner is spun twice, what is the probability that the spinner will stop on a consonant and then again on a consonant?
The spinner is a circle divided into 6 equal sections. The sections are labeled L U Z O E and I. (1 point)
two-ninths
start fraction 1 over 3 end fraction
start fraction 1 over 6 end fraction
one-ninth
I chose 1/9
That is incorrect.
To solve this problem, we need to find the probability of spinning a consonant on the first spin. L, U, and Z are consonants, while O, E, and I are vowels, so there are three consonants out of a total of six sections:
P(consonant on first spin) = 3/6
After a consonant is spun on the first try, there are now only five sections left, since that section will be removed. Of those five sections, two are consonants (L and Z) and three are vowels (O, E, and I):
P(consonant on second spin given consonant on first spin) = 2/5
To find the probability of both events happening (spinning a consonant and then spinning a consonant again), we need to multiply the probabilities:
P(consonant on first spin) x P(consonant on second spin given consonant on first spin) = (3/6) x (2/5)
Simplifying, we get:
(3/6) x (2/5) = 1/5
Therefore, the correct answer is:
one-fifth
A box contains 4 yellow tiles, 6 green tiles, and 10 purple tiles. Without looking, you draw out a tile and then draw out a second tile without returning the first tile.
Find P(purple, then purple).
A) nine over thirty-eight
B) one-fourth
C) three-hundredths
D) three over nineteen
I chose B
That is incorrect.
To solve this problem, we need to find the probability of drawing a purple tile on the first draw, and then drawing another purple tile on the second draw without replacing the first tile.
The probability of drawing a purple tile on the first draw is:
P(purple on first draw) = 10/20
After the first tile is drawn, there will be 19 tiles remaining, of which 9 are purple.
The probability of drawing another purple tile on the second draw without replacing the first tile is:
P(purple on second draw given purple on first draw) = 9/19
To find the probability of both events happening (drawing a purple tile and then drawing another purple tile), we need to multiply the probabilities:
P(purple, then purple) = P(purple on first draw) x P(purple on second draw given purple on first draw)
P(purple, then purple) = (10/20) x (9/19)
Simplifying, we get:
P(purple, then purple) = 9/38
Therefore, the correct answer is:
A) nine over thirty-eight
In how many different ways can the following positions be chosen from the 18-member math team?
president, vice president, and treasurer
(1 point)
a)4,080
b) 306
c) 5,814
d) 4,896
I chose d
That is correct.
To solve this problem, we can use the permutation formula:
nPr = n! / (n - r)!
where n is the total number of members in the math team and r is the number of positions to be filled.
For the president position, we have 18 candidates to choose from.
After we've chosen the president, there are 17 candidates remaining for the vice president position.
Finally, after we've chosen the president and vice president, there are 16 candidates remaining for the treasurer position.
Therefore, the number of ways to choose a president, a vice president, and a treasurer from the math team is:
nPr = 18P3
= (18 x 17 x 16) / (3 x 2 x 1)
= 4,896
Therefore, the correct answer is:
d) 4,896