Answer:
a) P(A∩B) = 0.21
b) P(A∩B') = 0.0072
c) P(B'|A)=0.0072/0.2172=0.0331
Step-by-step explanation:
A = the gun will detect a speeder
B = driver is actually speeding
P(A|B) = 0.75
P(A|B')=0.01
P(B') = 0.72
a) by definition
P(A∩B)=P(A|B)*P(B)=0.75*(1-0.72)=0.21
b) by definition
P(A∩B')=P(A|B')*P(B')=0.01*(0.72)=0.0072
c)
by bayes theorem
P(B'|A)=P(A|B')*P(B')/P(A)
by total probability theorem
P(A)=P(A∩B)+P(A∩B')=0.21+0.0072=0.2172
so
P(B'|A)=0.0072/0.2172=0.0331
The probabilities asked in the question are calculated using basic principles of probability: a) the probability that the radar gun detects speeding and the driver was speeding is 21%, b) the probability that the radar gun detects speeding, and the driver was not speeding is 0.72%, c) given that a driver is stopped because the radar gun detected speeding, the probability that they were actually driving within the speed limit is 3.3%.
The probability of a speed detection can be divided into two different categories – the probability of an accurate detection (where the driver is actually speeding), and a false detection (where the driver is not speeding).
a. The probability that the gun detects speeding and the driver was speeding is calculated by the accuracy of the gun, which is 75%, multiplied by the percentage of drivers that are actually speeding. Given that 28% of the drivers exceed the speed limit (100% - 72% safe drivers), the probability is 0.75*0.28 = 0.21 or 21%.
b. The probability that the gun detects a speeder when the driver is not speeding is calculated by multiplying the probability the gun makes an error (1%) and the chance that the driver is driving within the speed limit (72%). So, 0.01*0.72 = 0.0072 or 0.72%.
c. If the police stop a driver because the gun detects speeding, the probability that the driver was actually driving safely is calculated by taking the probability that the gun gives a false speed reading (0.72%) and dividing it by the total probability that the gun detects a speeding vehicle (accurate detection + false detection = 21% + 0.72% = 21.72%). So, 0.72 / 21.72 = 0.033 or 3.3%.
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8) red and 1, red and 2, red and 3, blue and 1, blue and 2, blue and 3
So answer is 6
9) 0.5*1/3 = 0.17
10) 0.5*2/3 = 0.33
How many biscuits does each child get?
biscuits.
Gemma gets
biscuits and Zak gets
Answer:
Gemma gets 3 biscuits
Zak gets 18 biscuits
Step-by-step explanation:
1:6 = 1+6
= 7
1/7 * 21 = 3
6/7 * 21 = 18
Step-by-step explanation:
x+6x=21
7x=21
x=3
6x=3×6= 18
Gemma gets 3 and Zak got 18
The fraction is closer to 1/2 than to 0 or 1 is 8/12.
The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
Given:
First Fraction
2/12 = 1/6 = 0.1667
Second Fraction
3/12
= 0.25
Third Fraction
8/12
= 0.6667
Fourth Fraction
10/12
= 0.83333
So, Fraction closer to 1/2 or 0.5 is 8/12.
Learn more about fraction here:
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In this situation I would convert the 1/2 into a fraction that has a common denominator. 1/2 will now be 6/12.
I think the best answer here is 8/12 because 6/12 is only two lines away from 8/12 where as everything else is either closer to 1 or 0.
I hope this helps. Good luck.
(blank) (blank) y (blank) (blank)
Options: 3, 6, -2, -∞, 12, ∞
<, ≤
Answer:
Range : (-∞, 12] Or -∞ < x ≤ 12.
Step-by-step explanation:
Domain of function is represented by the x-values (input values) of the function given in the graph.
Similarly, Range of the function is define by the y-values (output values) on the graph of a function.
Since y-values on the graph are between 12 and negative infinity (Including 12),
Therefore, range of the function will be (-∞, 12] or -∞ < x ≤ 12
Answer:
-∞ < y ≤ 12
Step-by-step explanation:
For all Plato users
Answer:
Step-by-step explanation:
The "fundamental theorem of algebra" says a polynomial of degree n will have n zeros. If the polynomial has real coefficients, the complex zeros will appear in conjugate pairs.
The graph of this quadratic (degree = 2) does not cross the x-axis, so there are no real values of x that make y=0. That means the two zeros are both complex.