The bascule bridge shown is opening from its horizontal position to its fully vertical position. So far, the bridge has lifted 3
1 answer:
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Answer:
(1) The value of P (A) is 0.4286.
(2) The value of P (B) is 0.50.
(3) The value of P (A ∩ B) is 0.2143.
(4) The the value of P (B|A) is 0.50.
(5) The events <em>A</em> and <em>B</em> are independent.
Step-by-step explanation:
The events are defined as follows:
<em>A</em> = a student in the class has a sister
<em>B</em> = a student has a brother
The information provided is:
<em>N</em> = 210
n (A) = 90
n (B) = 105
n (A ∩ B) = 45
The probability of an event <em>E</em> is the ratio of the favorable number of outcomes to the total number of outcomes.
The conditional probability of an event <em>X</em> provided that another event <em>Y</em> has already occurred is:
If the events <em>X</em> and <em>Y</em> are independent then,
(1)
Compute the probability of event <em>A</em> as follows:
The value of P (A) is 0.4286.
(2)
Compute the probability of event <em>B</em> as follows:
The value of P (B) is 0.50.
(3)
Compute the probability of event <em>A</em> and <em>B</em> as follows:
The value of P (A ∩ B) is 0.2143.
(4)
Compute the probability of <em>B</em> given <em>A</em> as follows:
The the value of P (B|A) is 0.50.
(5)
The value of P (B|A) = 0.50 = P (B).
Thus, the events <em>A</em> and <em>B</em> are independent.
V1 - velocity first train
v2 - velocity second train
v2 > v1
v2 - v1 = 17 mph
We know, that:
![s_1+s_2=210 \ [miles] \\ \\ t_1=t_2=2h](https://tex.z-dn.net/?f=s_1%2Bs_2%3D210%20%5C%20%5Bmiles%5D%20%5C%5C%20%5C%5C%20t_1%3Dt_2%3D2h)
So:
NOw we've got simple system of equations:
![+\begin{cases} v_2-v_1=17 \\ v_2+v_1=105\end{cases} \\ \\ 2v_2=122 \qquad /:2 \\ \\ v_2=61 \qquad [mph] \\ \\ v_2-v_1=17 \\ \\ 61-v_1=17 \\ \\ v_1=44](https://tex.z-dn.net/?f=%2B%5Cbegin%7Bcases%7D%20v_2-v_1%3D17%20%5C%5C%20v_2%2Bv_1%3D105%5Cend%7Bcases%7D%20%5C%5C%20%5C%5C%202v_2%3D122%20%5Cqquad%20%2F%3A2%20%5C%5C%20%5C%5C%20v_2%3D61%20%5Cqquad%20%5Bmph%5D%20%5C%5C%20%5C%5C%20v_2-v_1%3D17%20%5C%5C%20%5C%5C%2061-v_1%3D17%20%5C%5C%20%5C%5C%20v_1%3D44)
Velocities of these trains are 61mph and 44mph
v2 - velocity second train
v2 > v1
v2 - v1 = 17 mph
We know, that:
So:
NOw we've got simple system of equations:
Velocities of these trains are 61mph and 44mph