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steposvetlana [31]
2 years ago
14

This season, the probability that the Yankees will win a game is 0.48 and the probability that the Yankees will score 5 or more

runs in a game is 0.57. The probability that the Yankees win and score 5 or more runs is 0.38. What is the probability that the Yankees lose and score fewer than 5 runs? Round your answer to the nearest thousandth.
Mathematics
1 answer:
gavmur [86]2 years ago
3 0

Answer:

0.33

Step-by-step explanation:

We can think of this in tems of a venn diagram.

We have a rectangle, which represents the probabilities combined, which is 1.

Then we have two interlocking circles, the first representing the probability the yankees win, the second representing the probability the yankes score 5 or more runs, and the overlap representing the probability of both.

Therefore, the probability of losing and scoring less than 5 runs must be the area outside the circles but inside the rectangle.

The union of 'winning' and 'scoring 5 or more runs' is equal to the sum of the probability of either, minus the probability of both, which is 0.48+0.57-0.38 = 0.67.

Therefore the probability neither happen is 1-0.67 = 0.33

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Hence Distance traveled at speed 115 mph is <u>345 miles</u> and Distance traveled at speed 105 mph is <u>210 miles</u>.

Step-by-step explanation:

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Total Distance = 555 mile

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Let time taken to travel at 115 mph be t

So Time taken to travel at 105 mph will be equal to difference between Total time and  time taken to travel at 115 mph.

Time taken to travel at 105 mph = 5-t

Distance traveled in speed 105 mph will be equal to speed multiplied by time taken to travel at 105 mph.

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Framing in equation form we get;

Distance traveled in 105 mph = 105(t-5) = 105t - 525

Now Total Distance traveled is equal sum of Distance traveled in 115 mph and Distance traveled in speed 105 mph

115t-(105t-525)=555\\\\115t-105t+525=555\\\\10t+525=555\\\\10t=555-525\\\\10t=30\\\\t=\frac{30}{10}=3

Time taken to travel at 115 mph = 3 hrs.

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Now Distance traveled in 115 mph = 115t = 115 \times 3 = 345\ miles

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