Probability Test

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Probability Test - 24

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Weekly Quiz Competition

Question 1
1 / -0

Two dices are thrown simultaneously. What is the probability of getting two numbers whose product is even?

A
$$\dfrac{1}{4}$$

B
$$\dfrac{3}{4}$$

C
$$\dfrac{1}{2}$$

D
$$\dfrac{1}{8}$$

Solution

Possible outcomes when dice are thrown simultaneously are :-
$$(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)$$
$$(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)$$
$$(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)$$
$$(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)$$
$$(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)$$
$$(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)$$
Favourale outcomes i.e. two numbers whose product is even are :
$$(1,2) (1,4) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,2) (3,4) (3,6) (4,1)$$
$$(4,2)(4,3) (4,4) (4,5) (4,6) (5,2) (5,4) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)$$
So,the probability of getting two numbers whose product is even is
$$ P(E)27/36 = 3/4$$
Question 2
1 / -0

Suppose you drop a coin at a random in a rectangular region shown in the figure. What is the probability that it will land inside the circle with diameter $$4$$ $$cm$$?

A
$$\dfrac{4 \pi}{75}$$

B
$$\dfrac{2 \pi}{75}$$

C
$$\dfrac{2}{75}$$

D
$$\dfrac{8 \pi }{75}$$
Question 3
1 / -0

Suppose you drop a pen at random in circular region with two concentric circles as shown in the figure. What is the probability that it will land inside the smaller circle?

A
$$\dfrac{ \pi r}{R}$$

B
$$\dfrac{ \pi r^2}{R}$$

C
$$\dfrac{ \pi r}{R^2}$$

D
$$\dfrac{ r^2}{R^2}$$

Solution
Question 4
1 / -0

In a Jungle which is rectangular in shape having sides $$20$$ $$km$$ and $$16$$ $$ km$$ , there is a square lake of side $$5 $$ $$km$$. An aeroplane crashes in the Jungle.Find the probability that it crashes in the lake.

A
$$\dfrac{25}{320}$$

B
$$\dfrac{25}{300}$$

C
$$\dfrac{20}{320}$$

D
$$\dfrac{22}{320}$$

Solution
Question 5
1 / -0

Suppose you drop a coin at a random in a rectangular region shown in the figure. What is the probability that it will land inside the circle with diameter $$0.5$$ meter?

A
$$\dfrac{\pi }{94}$$

B
$$\dfrac{ \pi }{96}$$

C
$$\dfrac{ \pi }{98}$$

D
none of these

Solution
Question 6
1 / -0

Suppose you drop a coin at a random in a rectangular region shown in the figure. What is the probability that it will land inside the circle with diameter $$25$$ $$cm$$?

A
$$\dfrac{ \pi }{94}$$

B
$$\dfrac{ \pi }{384}$$

C
$$\dfrac{\pi }{84}$$

D
none of these

Solution
Question 7
1 / -0

Suppose you drop a coin at random in circular region with two concentric circles as shown in the figure. What is the probability that it will land inside the larger circle which is not a part of smaller circle (circular ring formed from these two circles)?

A
$$\dfrac{56}{81}$$

B
$$\dfrac{56 \pi }{81}$$

C
$$\dfrac{25}{81}$$

D
$$\dfrac{25 \pi}{81}$$

Solution
Question 8
1 / -0

Suppose you drop a metal pin at random in circular region with two concentric circles of radii $$5cm$$ and $$8cm$$. What is the probability that it will land inside the larger circle which is not a part of smaller circle (circular ring formed from these two circles)?

A
$$\dfrac {25}{64}$$

B
$$\dfrac {25 \pi}{64}$$

C
$$\dfrac {39 \pi}{64}$$

D
none of these

Solution
Question 9
1 / -0

Find the probability that a randomly chosen point from figure lies in the shaded region.

A
0.775

B
0.786

C
0.765

D
0.785

Solution
Question 10
1 / -0

$$ABCD$$ is a square having side $$4$$ $$cm$$. $$P$$ is the mid point of $$BC$$ and $$Q$$ is the mid point of $$CD$$.A point is selected at random from the square.The probability that the point lies inside the triangle $$PCQ$$ is

A
$$\dfrac{1}{10}$$

B
$$\dfrac{2}{8}$$

C
$$\dfrac{1}{8}$$

D
$$\dfrac{1}{4}$$