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nekit [7.7K]
3 years ago
11

Four teams A,B,C, and D compete in a tournament, and exactly one of them will win the tournament. Teams A and B have the same ch

ance of winning the tournament. Team C is twice as likely to win the tournament as team D. The probability that either team A or team C wins the tournament is 0.6. Find the probabilities of each team winning the tournament.
Mathematics
1 answer:
beks73 [17]3 years ago
4 0

Answer:

A= 0,2

B= 0,2

C= 0,4

D=0,2

Step-by-step explanation:

We know that only one team can win, so the sum of each probability of wining  is one

P(A)+P(B)+P(C)+P(D)=1

then we Know that the probability of Team A and B are the same, so

P(A)=P(B)

And that the  the probability that either team A or team C wins the tournament is 0.6, so P(A)+Pc)= 0,6, then P(C)= 0.6-P(A)

Also, we know that team C is twice as likely to win the tournament as team D, so P(C)= 2 P(D) so P(D) = P(C)/2= (0.6-P(A))/2

Now if we use the first formula:

P(A)+P(B)+P(C)+P(D)=1

P(A)+P(A)+0.6-P(A)+(0.6-P(A))/2=1

0,5 P(A)+0.9=1

0,5 P(A)= 0,1

P(A)= 0,2

P(B)= 0,2

P(C)=0,4

P(D)=0,2

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I need this answered Fast if possible. A car is traveling on a small highway and is either going 55 miles per hour or 35 miles
Alex787 [66]

a. It spends about 2.045 hours going 55 miles per hour

b. It spends 1 hour going 35 miles per hour

c. The trip would take about 3.64 hours

Step-by-step explanation:

A car is traveling on a small highway and is either going 55 miles per hour or 35 miles  per hour, depending on the speed limits, until it reaches its destination 200 miles  away

  • x represents the amount of time in hours that the car is going 55 miles per  hour
  • y represents the amount of time in hours that the car is going 35 miles per hour
  • The equation  that describing the relationship is 55x + 35y = 200

We need to find:

a. How long does it  spend going 55 miles per hour, if the car spends 2.5 hours going 35 miles per hour on the trip

∵ 55x + 35y = 200

∵ The car spends 2.5 hours going 35 miles per hour on the trip

∵ y represents the amount of time that the car going 35 mi./h

∴ y = 2.5

- Substitute the value of y in the equation to find the value of x

∴ 55x + 35(2.5) = 200

∴ 55x + 87.5 = 200

- Subtract 87.5 from both sides

∴ 55x = 112.5

- Divide both sides by 55

∴ x = 2.045 hours

It spends about 2.045 hours going 55 miles per hour

b.how long does it  spend going 35 miles per hour, if the car spends 3 hours going 55 miles per hour on the trip

∵ 55x + 35y = 200

∵ The car spends 3 hours going 55 miles per hour on the trip

∵ x represents the amount of time that the car going 55 mi./h

∴ x = 3

- Substitute the value of y in the equation to find the value of x

∴ 55(3) + 35y = 200

∴ 165 + 35y = 200

- Subtract 165 from both sides

∴ 35y = 35

- Divide both sides by 35

∴ y = 1 hour

It spends 1 hour going 35 miles per hour

c. How long would the trip take, if the car spends no time going 35 miles per hour

∵ 55x + 35y = 200

∵ The car spends no time going 35 miles per hour

∴ y = 0

- Substitute the value of y in the equation to find the value of x

∴ 55x + 35(0) = 200

∴ 55x  = 200

- Divide both sides by 55

∴ x = 3.63 hours

The trip would take about 3.64 hours

Learn more:

You can learn more about the equations in brainly.com/question/4097107

#LearnwithBrainly

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Step-by-step explanation:

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Step-by-step explanation:

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So,

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