6.Suppose you have a drawer full of white, black, and yellow pairs of socks. If the probability of picking a white pair of socks is 4/9, and the probability of picking a black pair of socks is 7/18, what is the probability of picking a yellow pair of socks?
a. 1/6
b 5/25
c 7/15
d 16/27
suppose the probability that it rains in the next two days is 1/3 for tomorrow and 1/6 for the day after tomorrow.What is P(rain tomorrow, then rain the day after tomorrow)?
A. 1/2
B.1/18***
C.2/9
D.1/9
Elizabeth has two identical number cubes. Both cubes have faces numbered 1 through 6. If elizabeth rolls each cube once, what is the probability that the sum of the two numbers on the top faces will be 10?
A. 1/36
b 1/12
c. 1/10
d 1/9
how many different arrangements can be made with the letters from the word TOPIC?
a. 3,125
b. 10
c.24
d.120
Ariel wants to choose 5 players for her basketball team. There are 7 players to choose from.How many different teams can Ariel make?
A. 21
B.32
c.42
D.56
Write the number of permutations in factorial form, then simplify. How many differnet ways can you and four of your friends sit in the backseat of a limousine?
A. 4!;24
b.4!120
C.5! 120
D. 5! 720
I already answered most of these.
To answer the first question, we need to find the probability of picking a yellow pair of socks. We know that the probability of picking a white pair of socks is 4/9 and the probability of picking a black pair of socks is 7/18.
To find the probability of picking a yellow pair of socks, we can subtract the sum of the probabilities of picking white and black pairs from 1, since these are the only options.
Probability of picking a yellow pair of socks = 1 - (Probability of picking a white pair + Probability of picking a black pair)
= 1 - (4/9 + 7/18)
= 1 - (8/18 + 7/18)
= 1 - 15/18
= 3/18
= 1/6
Therefore, the probability of picking a yellow pair of socks is 1/6.
For the second question, we need to find the probability of rain occurring on both tomorrow and the day after tomorrow. The probability of rain tomorrow is given as 1/3, and the probability of rain the day after tomorrow is given as 1/6.
To find the probability of both events occurring, we can multiply the probabilities together.
Probability of rain tomorrow and rain the day after tomorrow = Probability of rain tomorrow * Probability of rain the day after tomorrow
= 1/3 * 1/6
= 1/18
Therefore, the probability of rain occurring tomorrow and the day after tomorrow is 1/18.
The third question asks for the probability of rolling two number cubes and getting a sum of 10. Each cube has faces numbered 1 through 6, so we need to find the number of ways to get a sum of 10 using the possible outcomes.
To get a sum of 10, we can have the following combinations:
- (4, 6)
- (5, 5)
- (6, 4)
These are the only three combinations that add up to 10. Since there are a total of 6 * 6 = 36 possible outcomes, the probability of getting a sum of 10 is:
Probability of getting a sum of 10 = Number of desired outcomes / Total number of possible outcomes
= 3 / 36
= 1 / 12
Therefore, the probability of rolling two number cubes and getting a sum of 10 is 1/12.
To find the number of different arrangements that can be made with the letters from the word "TOPIC," we need to calculate the number of permutations.
The word "TOPIC" has 5 letters, so there are 5 choices for the first letter, 4 choices for the second letter, 3 choices for the third letter, 2 choices for the fourth letter, and 1 choice for the last letter.
Therefore, the number of different arrangements is:
Number of arrangements = 5!
= 5 * 4 * 3 * 2 * 1
= 120
So, there are 120 different arrangements that can be made with the letters from the word "TOPIC."
For the fifth question, Ariel wants to choose 5 players for her basketball team out of 7 players. We need to calculate the number of different teams that can be made.
Using the concept of combinations, the number of different teams can be calculated as:
Number of teams = C(7, 5)
= 7! / (5! * (7-5)!)
= 7! / (5! * 2!)
= (7 * 6 * 5 * 4 * 3) / (2 * 1)
= 42
Therefore, Ariel can make 42 different teams.
For the last question, we need to calculate the number of different ways you and your four friends can sit in the backseat of a limousine. The order in which you sit matters, so we need to find the number of permutations.
Since there are 5 people, the number of permutations can be calculated as:
Number of permutations = 5!
= 5 * 4 * 3 * 2 * 1
= 120
Therefore, there are 120 different ways you and your four friends can sit in the backseat of a limousine.
my answers r
1,d
2,c
3,a
4.c
5.b
6.d
Ariel wants to choose 5 players for her basketball team. There are 7 players to choose from.How many different teams can Ariel make?
A. 21
B.32
c.42
D.56
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combinations in grade seven?
C(n,r) = n!/[r!(n-r)!]
= 7!/[5!(2!)]
= 7*6/2
=21
========================
Write the number of permutations in factorial form, then simplify. How many differnet ways can you and four of your friends sit in the backseat of a limousine?
A. 4!;24
b.4!120
C.5! 120
D. 5! 720
There are 5 of you.
Order does not matter so permutations of 5 taken 5 at a time
5!
=5*4*3*2 = 120
Write the number of permutations in factorial form, then simplify. How many differnet ways can you and four of your friends sit in the backseat of a limousine?
A. 4!;24
b.4!120
C.5! 120
D. 5! 720
There are 5 of you.
Order does matter so permutations of 5 taken 5 at a time
5!
=5*4*3*2 = 120