Probability Test

Result

Probability Test - 23

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

If a leap year is selected at random what is the probability that it will contain $$53$$ Tuesdays?

A
$$\dfrac{1}{7}$$

B
$$\dfrac{2}{7}$$

C
$$\dfrac{3}{7}$$

D
$$\dfrac{4}{7}$$

Solution

$$1 year = 365$$ days
A leap year has $$366$$ days
A year has $$52$$ weeks. Hence there will be 52 Tuesdays for sure.
$$52 weeks = 52 \times 7 = 364 days$$
$$366 – 364 =2$$ days
In a leap year there will be 52 Tuesdays and 2 days will be left.
These 2 days can be:
Sunday, Monday
Monday, Tuesday
Tuesday, Wednesday
Wednesday, Thursday
Thursday, Friday
Friday, Saturday
Saturday, Sunday
Of these total 7 outcomes, the favorable outcomes are 2.
Hence the probability of getting 53 Tuesdays in a leap year $$P(E)=\frac{2}{7}$$
Question 2
1 / -0

A pair of dice is thrown. Find the probability of getting a sum of $$8$$ or getting an even number on both the dices.

A
$$\dfrac{5}{36}$$

B
$$\dfrac{9}{36}$$

C
$$\dfrac{11}{36}$$

D
$$\dfrac{13}{36}$$

Solution

Sample space for total number of possible outcomes
{$$(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)$$
$$(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)$$,
$$(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)$$,
$$(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)$$,
$$(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)$$,
$$(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)$$}
Total number of outcomes = $$36$$
Favorable outcomes for sum of $$8$$ or getting an even number on both the dices are
$${(2, 6), (3, 5), (4, 4), (5, 3), (6, 2), (2, 2), (2, 4), (4, 2), (4, 6), (6, 4), (6, 6)}$$
Number of favorable outcomes = $$11$$
The probability of getting a sum of $$8$$ or getting an even number on both the dices, $$P(E)=\dfrac {n(E)}{n(S)}=\dfrac {11}{36}$$
Question 3
1 / -0

From a batch of $$100$$ items of which $$20$$ are defective, exactly two items are chosen, one at a time, without replacement. Calculate the probability that the first item chosen is defective.

A
$$\dfrac{20}{100}$$

B
$$\dfrac{20}{120}$$

C
$$\dfrac{2}{100}$$

D
none of these

Solution

Let $$A$$={first item chosen is defective}, $$B$$ ={second item chosen is defective}

Given:

Total number of items $$=100$$.

NUmber of defective items $$=20$$

To find:

the probabilities that the first item is chosen is defective

$$P(A)=\dfrac {\text{Number of items defective}}{\text{total number of items}}=\dfrac {20}{100}=\dfrac 15$$
Question 4
1 / -0

List the outcomes in the experiment of tossing two coins together.

A
When two coins are tossed together, the possible outcomes of the experiment are $$HT$$ and $$TH$$

B
When two coins are tossed together, the possible outcomes of the experiment are $$HH$$ and $$TT$$.

C
When two coins are tossed together, the possible outcomes of the experiment are $$HH, HT, TH$$ and $$TT$$.

D
None of these

Solution

The outcome of a throw of coin can be only head or tails.
Coin $$1=T,H$$
Coin $$2=T,H$$
The coins together $$=TT,HH,TH,HT$$
Question 5
1 / -0

Two dice are thrown simultaneously. Find the probability of getting a multiple of $$2$$ on one dice and a multiple of $$3$$ on the other.

A
$$\dfrac{9}{36}$$

B
$$\dfrac{10}{36}$$

C
$$\dfrac{11}{36}$$

D
$$\dfrac{5}{36}$$

Solution

Total number of possible cases $$= 36$$
Favourable cases of getting multiple of $$2$$ on one dice and a multiple of $$3$$ on the other
$$= \{(2, 3), (2,6), (3, 2), (3, 4), (3,6), (4, 3), (4, 6), (6, 2), (6, 3), (6,4), (6, 6)\}$$
Total number of favourable cases $$= 11$$
P (multiple of $$2$$ on one dice and a multiple of $$3$$ on other dice) $$= \displaystyle \frac{11}{36}$$
Question 6
1 / -0

A die is dropped at random on the rectangular region of length $$3\ m$$ and breadth $$2\ m$$ as shown in figure What is tile probability that it will land inside the circle with diameter $$1\ m$$ ?

A
$$\frac{\pi}{24}$$

B
$$\frac{2\pi}{24}$$

C
$$\frac{\pi}{25}$$

D
None of these
Question 7
1 / -0

A dice is thrown once. Find the probability of getting a number greater than $$4$$.

A
$$\dfrac{1}{5}$$

B
$$\dfrac{1}{4}$$

C
$$\dfrac{1}{3}$$

D
$$\dfrac{1}{2}$$

Solution

$${\textbf{Step-1: Write sample space and event.}}$$

$${\text{Let S be the sample space.}}$$

$${\text{S= {1, 2, 3, 4, 5, 6}}}$$

$$\Rightarrow n(S) =6$$

$${\text{Let A be the event getting number greater than 4.}}$$

$${\text{A= { 5, 6}}}$$

$$\Rightarrow n(A) =2.$$

$${\textbf{Step-2: Find probability.}}$$

$${\text{Let P be the probability of getting a number greater than 4.}}$$
$$\Rightarrow P(A)= \dfrac{n(A)}{n(S)}$$

$$\Rightarrow P(A)= \dfrac{2}{6}$$

$$\Rightarrow P(A)= \dfrac{1}{3}.$$

$${\textbf{Hence, option C is correct.}}$$
Question 8
1 / -0

A die is thrown once.find the probability of getting a prime number less than $$5.$$

A
$$\dfrac{7}{3}$$

B
$$\dfrac{5}{3}$$

C
$$\dfrac{2}{3}$$

D
$$\dfrac{1}{3}$$

Solution

Sample space of throwing
a die once $$=\{1, 2, 3, 4, 5, 6\}$$.
Prime no. less than $$5=\{2, 3\}$$.
Probability $$=\dfrac{Favourable\ outcomes}{Total\ outcomes}=\dfrac{2}{6}=\dfrac{1}{3}$$.
Question 9
1 / -0

A die is thrown .The probability that the number comes up even is ______ .

A
$$\dfrac{1}{2}$$

B
$$\dfrac{1}{3}$$

C
$$\dfrac{1}{4}$$

D
$$\dfrac{1}{5}$$

Solution

Possible Outcomes of a Dice $$= 1, 2, 3, 4, 5, 6$$
Even Outcomes $$= 2, 4, 6$$
Probability of an event $$P(E) = \dfrac{No.\ of\ Favourable\ Outcomes}{Total\ No.\ of\ Outcomes}$$

Here,
Favourable Outcomes $$=$$ Getting an Even Number on Dice
Number of Favourable Outcomes $$=$$ Number of Possible Even Outcomes $$= 3$$
Total Number of Outcomes $$= 6$$

$$\Rightarrow P(E) = \dfrac{3}{6} = \dfrac{1}{2}$$
Question 10
1 / -0

A pair of dies is thrown, find the probability of getting a total of numbers is more than $$10$$.

A
$$1/5$$

B
$$1/12$$

C
$$1/4$$

D
$$2/7$$

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Probability Test - 23

Result

Probability Test - 23

Score

-

Rank

-

SHARING IS CARING

Question 1

$$\dfrac{1}{7}$$

$$\dfrac{2}{7}$$

$$\dfrac{3}{7}$$

$$\dfrac{4}{7}$$

Solution

Question 2

$$\dfrac{5}{36}$$

$$\dfrac{9}{36}$$

$$\dfrac{11}{36}$$

$$\dfrac{13}{36}$$

Solution

Question 3

$$\dfrac{20}{100}$$

$$\dfrac{20}{120}$$

$$\dfrac{2}{100}$$

none of these

Solution

Question 4

When two coins are tossed together, the possible outcomes of the experiment are $$HT$$ and $$TH$$

When two coins are tossed together, the possible outcomes of the experiment are $$HH$$ and $$TT$$.

When two coins are tossed together, the possible outcomes of the experiment are $$HH, HT, TH$$ and $$TT$$.

None of these

Solution

Question 5

$$\dfrac{9}{36}$$

$$\dfrac{10}{36}$$

$$\dfrac{11}{36}$$

$$\dfrac{5}{36}$$

Solution

Question 6

$$\frac{\pi}{24}$$

$$\frac{2\pi}{24}$$

$$\frac{\pi}{25}$$

None of these

Question 7

$$\dfrac{1}{5}$$

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

$$\dfrac{1}{3}$$

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

Solution

Question 8

$$\dfrac{7}{3}$$

$$\dfrac{5}{3}$$

$$\dfrac{2}{3}$$

$$\dfrac{1}{3}$$

Solution

Question 9

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

$$\dfrac{1}{3}$$

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

$$\dfrac{1}{5}$$

Solution

Question 10

$$1/5$$

$$1/12$$

$$1/4$$

$$2/7$$

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.