The bumper car ride at the state fair has 2 red cars, 4 green cars, an for the ride and is assigned a the probability that both
1 answer:
Answer:
a) 3.6%
Step-by-step explanation:
The given question mixed up, below is the correct question:
The bumper car ride at the state fair has 2 red cars, 4 green cars, and 2 blue cars. Garth is first in line for the ride and is assigned a car at random. Patty is next in line and is randomly assigned a car. Find the probability that both events A and B occur. Express your answer as a percent. If necessary, round your answer to the nearest tenth.
Calculation:
Given that the state fair has 2 red cars, 4 green cars and 2 blue cars.
There are therefore 2+4+2 = 8 cars in total.
Probability that Events A occurs P(A) = = 4
Probability that Events B occurs P(B) =
Probability that Events A and B occur P(A ∩ B) = ×
=
= 0.0357 = 3.57% ≈ 3.6%
Therefore, the probability that both events A and B occur is 3.6%
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The value of a is 184. The above solution is derived using Pythagoras' theorem .
We let O be the center, A₁ A A₂ , B₁ B B₂ represent the chords with length 10, 14 respectively.
Connecting the endpoints of the chords with the center, we have several right triangles. However, we do not know whether the two chords are on the same side or different sides of the center of the circle.
By the Pythagorean Theorem on Δ OBB₁,
we get
, where x is the length of the other leg. Now the length of the leg of Δ OAA₁ is either 6 + x or 6 - x depending whether or not A₁A₂, B₁B₂ are on the same side of the center of the circle:
Only the negative works here (thus the two chords are on opposite sides of the center), and solving we get x = 1, r = .
The leg formed in the right triangle with the third chord is 3 - x = 2, and by the Pythagorean Theorem again,
⇒
a = 184
Hence,
The value of a is 184.
Learn more about Pythagoras theorem from the given link
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