Probability Test

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Probability Test - 16

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Weekly Quiz Competition

Question 1
1 / -0

When a coin is tossed at random, then the probability of getting a head is ________.

A
$$0$$

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

C
$$1$$

D
$$2$$

Solution

Tossing of a coin at random can give only two results, i.e. Heads or Tails.
$$\Rightarrow$$ Total number of outcomes possible $$= 2$$

Probability $$= \dfrac{\text{Favourable Outcomes}}{\text{Total Outcomes}} = \dfrac{1}{2}$$
Question 2
1 / -0

Two men hit at a target with probabilities $$\dfrac{1}{2}$$ and $$\dfrac{1}{3}$$ respectively. What is the probability that exactly one of them hits the target?

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

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

C
$$\dfrac{1}{6}$$

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

Solution

$${ E }_{ 1 }$$ denotes the event when first man hits the target
$${ E }_{ 2}$$ denotes the event when second man hits the target
$$P({ E }_{ 1 })=\cfrac { 1 }{ 2 } ,P({ E }_{ 2 })=\cfrac { 1 }{ 3 } $$
Probability that exactly one of them hits the target, $$P=P({ E }_{ 1 })P({ \overset { \_ }{ E } }_{ 2 })+P({ E }_{ 2 })P({ \overset { \_ }{ E } }_{ 1 })$$
$$=\dfrac { 1 }{ 2 } \times \dfrac { 2 }{ 3 } +\dfrac { 1 }{ 3 } \times \dfrac { 1 }{ 2 } =\dfrac { 1 }{ 2 } $$
Question 3
1 / -0

In a single throw of a die, the probability of getting a multiple of $$3$$ is ____________.

A
$$\displaystyle\frac{1}{2}$$

B
$$\displaystyle\frac{1}{3}$$

C
$$\displaystyle\frac{1}{6}$$

D
$$\displaystyle\frac{3}{4}$$

Solution

Possible outcomes on rolling a dice are $$1,2,3,4,5,6$$
Out of the possible outcomes, multiple of $$3$$ are $$3$$ and $$6$$.

Probability $$=$$ Favourable Outcomes $$\div$$ Total Outcomes $$= \dfrac{2}{6} = \dfrac{1}{3}$$
Question 4
1 / -0

A die is tossed $$80$$ times and the number $$3$$ is obtained $$14$$ times. Now, a dice is tossed at random, then the probability of getting the number $$3$$ is ________.

A
$$\dfrac {7}{40}$$

B
$$\dfrac {3}{14}$$

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

D
$$\dfrac {3}{40}$$

Solution

Total number of times dice was rolled $$= 80$$
Number of times $$3$$ is obtained $$= 14$$

Probability $$= \dfrac{\text{Favourable Outcomes}}{\text{Total Outcomes}}$$

$$\Rightarrow$$ Probability of obtaining $$3 = \dfrac{14}{80} =\dfrac{7}{40}$$
Question 5
1 / -0

A die is thrown $$400$$ times, the frequency of the outcomes of the events are given as under.
outcome
$$1$$
$$2$$
$$3$$
$$4$$
$$5$$
$$6$$
Frequency
$$70$$
$$65$$
$$60$$
$$75$$
$$63$$
$$67$$
Find the probability of occurrence of an odd number.

A
The probability of occurrence of odd number$$=\dfrac{5}{7}$$

B
The probability of occurrence of odd number$$=\dfrac{9}{2}$$

C
The probability of occurrence of odd number$$=\dfrac{193}{400}$$

D
The probability of occurrence of odd number$$=\dfrac{200}{299}$$

Solution

Sum of frequencies $$= 400 $$

Odd numbers are $$1, 3, 5$$

Therefore, frequency of all odd numbers $$= 70 + 60 + 63 = 193 $$

$$P(\text{event})=\dfrac{\text{Frequency of occurring of event}}{\text{The total number of trials}}$$

Therefore , probability of occurrence of odd number$$=\dfrac{193}{400}$$
Question 6
1 / -0

The probability that a two digit number selected at random will be a multiple of '$$3$$' and not a multiple of '$$5$$' is

A
$$\displaystyle \frac{2}{15}$$

B
$$\displaystyle \frac{4}{15}$$

C
$$\displaystyle \frac{1}{15}$$

D
$$\displaystyle \frac{4}{90}$$

Solution

$$\Rightarrow$$ Total number of two digit number $$=90$$

$$\Rightarrow$$ Total number of two digit number which is divisible by $$3=30$$

Out of this there are $$6$$ numbers divisible by $$15$$ $$(15,30,45,60,75,90)$$ which are also divisible by $$5.$$

$$\Rightarrow$$ Total two digit number which are divisible by $$3$$ but not $$5=30-6=24$$

$$\Rightarrow$$ Required probability $$=\dfrac{24}{90}=\dfrac{4}{15}$$
Question 7
1 / -0

On one page of a telephone directory there were $$200$$ telephone numbers. The frequency distribution of their unit place digit is given in the following table:
Digit $$0$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$
Frequency $$22$$ $$26$$ $$22$$ $$22$$ $$20$$ $$10$$ $$14$$ $$28$$ $$16$$ $$20$$

A

$$0.15$$

B

$$0.17$$

C

$$0.18$$

D
None of these

Solution

The probability that the digit in its unit place is more than $$ 7 = \dfrac {16+20}{200} =\dfrac {36}{200} = 0.18 $$
Question 8
1 / -0

In a survey of $$364$$ children aged $$19-36$$ months, it was found that $$91$$ liked to eat potato chips. If a child is selected at random, the probability that he/she does not like to eat potato chips is :

A
$$0.25$$

B
$$0.50$$

C
$$0.75$$

D
$$0.80$$

Solution

Favorable cases $$=364 - 91 =273$$
Total cases $$= 364$$
$$\therefore$$ Probability $$= \dfrac { 273 }{ 364 }=0.75$$
Question 9
1 / -0

A coin is tossed $$150$$ times and the outcomes are recorded. The frequency distribution of the outcomes $$H$$ (i.e., head) and $$T$$ (i.e., tail) is given below :
Outcome $$H$$ $$T$$
Frequency $$85$$ $$65$$
Find the value of $$P(H)$$, i.e., probability of getting a head in a single trial.

A
$$P(H) =0.769$$ (approx)

B
$$P(H) =0.663$$ (approx)

C
$$P(H) =0.567$$ (approx)

D
None of these

Solution

Total number of trials $$= 150$$
Chances or trials which favour the outcome $$H=85$$
$$P(H) =$$ $$ \displaystyle \frac{85}{150} $$ $$=$$ $$0.567$$ (approx)
Question 10
1 / -0

To know the opinion of the student about the subject statistic, a survey of $$200$$ students was conducted.
The data is recorded in the following table
Opinion Like Dislike
No. of Students $$135$$ $$65$$
Find the probability that a student chosen at random
$$(i)$$ likes statistics, $$(ii)$$ does not like it.

A
$$(i) \displaystyle \frac{13}{40} $$

$$(ii) \displaystyle \frac{19}{40} $$

B
$$(i) \displaystyle \frac{27}{40} $$

$$(ii) \displaystyle \frac{13}{40} $$

C
$$(i)\displaystyle \frac{17}{40} $$

$$(ii) \displaystyle \frac{29}{40} $$

D
None of these

Solution

Total number of students $$= 200$$
(i) Number of students who like the subject of statistics $$= 135$$
The probability that a student likes that subject $$=$$ $$ \displaystyle\frac{135}{200} $$$$ =$$ $$ \displaystyle \frac{27}{40} $$

(ii) Number of students who dislike the subject of statics $$=$$ 65
The probability that a student dislikes the subject $$=$$ $$ \displaystyle \frac{65}{200} $$ = $$ \displaystyle \frac{13}{40} $$

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Re-Attempt Weekly Quiz Competition

outcome	$$1$$	$$2$$	$$3$$	$$4$$	$$5$$	$$6$$
Frequency	$$70$$	$$65$$	$$60$$	$$75$$	$$63$$	$$67$$

Digit	$$0$$	$$1$$	$$2$$	$$3$$	$$4$$	$$5$$	$$6$$	$$7$$	$$8$$	$$9$$
Frequency	$$22$$	$$26$$	$$22$$	$$22$$	$$20$$	$$10$$	$$14$$	$$28$$	$$16$$	$$20$$

Outcome	$$H$$	$$T$$
Frequency	$$85$$	$$65$$

Opinion	Like	Dislike
No. of Students	$$135$$	$$65$$

Probability Test - 16

Result

Probability Test - 16

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Question 1

$$0$$

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

$$1$$

$$2$$

Solution

Question 2

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

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

$$\dfrac{1}{6}$$

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

Solution

Question 3

$$\displaystyle\frac{1}{2}$$

$$\displaystyle\frac{1}{3}$$

$$\displaystyle\frac{1}{6}$$

$$\displaystyle\frac{3}{4}$$

Solution

Question 4

$$\dfrac {7}{40}$$

$$\dfrac {3}{14}$$

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

$$\dfrac {3}{40}$$

Solution

Question 5

The probability of occurrence of odd number$$=\dfrac{5}{7}$$

The probability of occurrence of odd number$$=\dfrac{9}{2}$$

The probability of occurrence of odd number$$=\dfrac{193}{400}$$

The probability of occurrence of odd number$$=\dfrac{200}{299}$$

Solution

Question 6

$$\displaystyle \frac{2}{15}$$

$$\displaystyle \frac{4}{15}$$

$$\displaystyle \frac{1}{15}$$

$$\displaystyle \frac{4}{90}$$

Solution

Question 7

$$0.15$$

$$0.17$$

$$0.18$$

None of these

Solution

Question 8

$$0.25$$

$$0.50$$

$$0.75$$

$$0.80$$

Solution

Question 9

$$P(H) =0.769$$ (approx)

$$P(H) =0.663$$ (approx)

$$P(H) =0.567$$ (approx)

None of these

Solution

Question 10

$$(i) \displaystyle \frac{13}{40} $$$$(ii) \displaystyle \frac{19}{40} $$

$$(i) \displaystyle \frac{27}{40} $$$$(ii) \displaystyle \frac{13}{40} $$

$$(i)\displaystyle \frac{17}{40} $$$$(ii) \displaystyle \frac{29}{40} $$

None of these

Solution

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$$(i) \displaystyle \frac{13}{40} $$

$$(ii) \displaystyle \frac{19}{40} $$

$$(i) \displaystyle \frac{27}{40} $$

$$(ii) \displaystyle \frac{13}{40} $$

$$(i)\displaystyle \frac{17}{40} $$

$$(ii) \displaystyle \frac{29}{40} $$