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stich3 [128]
3 years ago
14

Carla can choose two of her three pairs of sneakers to take to a track meet. If the pairs of sneakers are called A, B, and C, wh

ich choice represents the sample space, S, for the event? S = {ABC} S = {ABC, CAB} S = {AB, AC, BC} S = {AB, BA, AC, CA, BC, CB}
Mathematics
2 answers:
Semenov [28]3 years ago
5 0
Number of ways of choosing two pair of sneakers from three pairs named A, B, C is given by 3C2 (3 combination 2) = 3! / 2!(3 - 2)! = 3! / (2! x 1!) = (3 x 2) / (2 x 1) = 3.

Therefore, the sample space is given by S = {AB, AC, BC}
Nuetrik [128]3 years ago
3 0
Its the third one hope this helps!!!!!!!!!
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A college student is taking two courses. The probability she passes the first course is 0.73. The probability she passes the sec
zhenek [66]

Answer:

b) No, it's not independent.

c) 0.02

d) 0.59

e) 0.57

f) 0.5616

Step-by-step explanation:

To answer this problem, a Venn diagram should be useful. The diagram with the information of Event 1 and Event 2 is shown below (I already added the information for the intersection but we're going to see how to get that information in the b) part of the problem)

Let's call A the event that she passes the first course, then P(A)=.73

Let's call B the event that she passes the second course, then P(B)=.66

Then P(A∪B) is the probability that she passes the first or the second course (at least one of them) is the given probability. P(A∪B)=.98

b) Is the event she passes one course independent of the event that she passes the other course?

Two events are independent when P(A∩B) = P(A) * P(B)

So far, we don't know P(A∩B), but we do know that for all events, the next formula is true:

P(A∪B) = P(A) + P(B) - P(A∩B)

We are going to solve for P (A∩B)

.98 = .73 + .66 - P(A∩B)

P(A∩B) =.73 + .66 - .98

P(A∩B) = .41

Now we will see if the formula for independent events is true

P(A∩B) = P(A) x P(B)

.41 = .73 x .66

.41 ≠.4818

Therefore, these two events are not independent.

c) The probability she does not pass either course, is 1 - the probability that she passes either one of the courses (P(A∪B) = .98)

1 - P(A∪B) = 1 - .98 = .02

d) The probability she doesn't pass both courses is 1 - the probability that she passes both of the courses P(A∩B)

1 - P(A∩B) = 1 -.41 = .59

e) The probability she passes exactly one course would be the probability that she passes either course minus the probability that she passes both courses.

P(A∪B) - P(A∩B) = .98 - .41 = .57

f) Given that she passes the first course, the probability she passes the second would be a conditional probability P(B|A)

P(B|A) = P(A∩B) / P(A)

P(B|A) = .41 / .73 = .5616

4 0
3 years ago
Solve h(x) = 5 - 9x Find h(8)
Alex_Xolod [135]

h(x) = 5 - 9x

h(8) = 5 - 9×8 ( putting value x = 8)

h(8) = 5 - 72

h(8) = -67

Answer is -67.

4 0
3 years ago
Read 2 more answers
The price of a cup of coffee was 2:40 yesterday today it Rose 265 find the<br> percentage increase
Anni [7]
N.B. I believe your question is saying that the price of a cup of coffee was $2.40 yesterday, and it rose to $2.65 today. Therefore, I will solve with these prices. 

The percent increase is 10.41666666% (The 6 is repeating.).

First, you find the difference, or increase, between the two prices.

New price - Old price = Increase

$2.65 - $2.40 = $0.25

The difference between the two prices is $0.25. To find the percent increase, you want to divide the original price ($2.40) from the increase ($0.25) and multiply by 100.

Increase ÷ Original Price × 100 = % increase

0.25 ÷ 2.40 × 100 = 10.41666666%

The percent increase is 10.41666666% (The 6 is repeating.).
6 0
4 years ago
Ethan was feeling adventurous at lunch. Rather than choosing a single drink, he decided to mix together all the drink choices. H
jarptica [38.1K]

Answer:

1.7

Step-by-step explanation:

I divided 7 by 12 to get 1.7. Each soda gets at least 1 ounce.

3 0
3 years ago
Read 2 more answers
The function g is given in three equivalent forms. Which form most quickly reveals the zeros (or "roots") of the function? Choos
koban [17]

Answer:

C. g(x) = -2 \cdot (x + 1)\cdot (x+7)

Step-by-step explanation:

The polynomial form that reveals most quickly the zeroes is the form of a product of binomials. That is:

g(x) = \Pi\limits_{i=1}^{n}  (x-r_{i})

Where \Pi is the product function and r_{i} is the i-th root of the polynomial.

Hence, g(x) = -2 \cdot (x + 1)\cdot (x+7) resembles a form that is close to the form described above. The right option is C.

8 0
3 years ago
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