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Answer:
Part A:
The probability that all of the balls selected are white:
Part B:
The conditional probability that the die landed on 3 if all the balls selected are white:
Step-by-step explanation:
A is the event all balls are white.
D_i is the dice outcome.
Sine the die is fair:
for i∈{1,2,3,4,5,6}
In case of 10 black and 5 white balls:
Part A:
The probability that all of the balls selected are white:
Part B:
The conditional probability that the die landed on 3 if all the balls selected are white:
We have to find
The data required is calculated above:
The exact measure of the angle is 45°.
<h3>How to get the angle?</h3>
We know that the terminal side passes through a point of the form (√2/2, y).
Notice that the point is on the unit circle, so its module must be equal to 1, so we can write:
We know that y is positive because the point is on the first quadrant.
Now, we know that our point is:
(√2/2, 1/√2)
And we can rewrite:
√2/2 = 1/√2
So the point is:
( 1/√2, 1/√2)
Finally, remember that a point (x, y), the angle that represents it is given by:
θ = Atan(y/x).
Then in this case, we have:
θ = Atan(1/√2/1/√2) = Atan(1) = 45°
If you want to learn more about angles, you can read: