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alex41 [277]
3 years ago
13

For a quarterback, the probability of throwing a completed pass is 60%, and the probability of gaining more than 10 yards on a r

unning play is 25%. What is the probability of gaining more than 10 yards on a running play and then throwing a completed pass? Express your answer as a decimal rounded to the nearest hundredth. What is the probability of throwing 3 completed passes in a row? Express your answer as a decimal rounded to the nearest hundredth.
Mathematics
1 answer:
never [62]3 years ago
3 0
The probability of gaining more than 10 yards then throwing a completed pass is 15%.

To find the chance of both events happening, you multiply the percents.
0.25 x 0.6 = 0.15 or 15%

The chance of throwing 3 completed passes would be:
0.6 x 0.6 x 0.6 = 0.216 or 21.6%
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It can be helpful to draw a diagram of the triangle we're concerned with. (See attached.)

We know the angle at the end of the shadow inside the triangle is 52°-22° = 30°. We assume the tree is growing straight up out of the hillside, so its angle with the hill inside the triangle is 90°+22° = 112°. Then the remaining angle between the shadow and the tree at the top of the tree is ...

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Now, we have the angle opposite the tree, and the angle opposite the known side length of the triangle (215 feet along the hill, AC in the diagram). This is enough information to usefully use the Law of Sines.

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