19. Case Study I
A helicopter is found missing in a rectangular region in the area shown below.
6 km
Laks
5 km-
- 2 km
-
9 km
1/4
을
in
a) The probability that the helicopter crashed inside the lake is-
1
5
27
7
i)
5
25
b) The Probability of an event always lie between-
i) O<P(E)</ ii) 1<P(E)<0 ii) P(E)<| iv)P(E)=1
c) The Probability of an event can never be-
1) Negative ii) positive. iii) lies between 0 and I iv) none of these
d) The probability of an impossible event is
i) 1
iii) 0
iv) infinite
e) The sum of the probabilities of the elementary events of an experiment is
i) 0
) 1
Answers
Answer:
a) the probability of helicopter crashed inside the lake is 5/27
Answer:
Step-by-step explanation:
Given that an apache helicopter of enemy is flying along the curve given by =x
2
+7
A soldier placed at (3,7) wants to shoot down the helicopter when it is nearest to him.
Now, the distance of the point from the soldier is
(x−3)
2
+(y−7)
2
Since the point lies on the curve y=x
2
+7
S=
(x−3)
2
+(x
2
+7−7)
2
→S=
x
4
+x
2
−6x+9
When the distance is maximum/minimum,
dx
dS
=0
→
(x
4
+x
2
−6x+9)
(4x
3
+2x−6)
=0
→4x
3
+2x−6=0
→2x
3
+x−3=0
→(x−1)×(2x
2
+2x+3)
The solutions to the above equation are
x=1,−0.5±i×0.5
5
Since the solution cannot have any complex roots.
Hence, x=1 is the abscissa of the nearest point to the soldier.
From equation 1, we get
y=1
2
+7
→y=8
So, the nearest point is (1,8)
Now, nearest distance S=
(1−3)
2
+(8−7)
2
→S=
(−2)
2
+(1)
2
→S=
4+1
→S=
5/27
units