Probability Test

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Probability Test - 15

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Question 1
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There are $$40$$ students in a class and their results is presented as below :
Result (Pass/Fail) Pass Fail
Number of Students $$30$$ $$10$$
If a student chosen at random out of the class, find the probability that the student has passed the examination

A
$$0.12$$

B
$$0.36$$

C
$$0.65$$

D
$$0.75$$

Solution

Total number of chances $$= 40$$
Chances or trials which favour a student to pass $$= 30$$
The probability of the required event, i.e., the student has passed the examination $$=$$ $$ \displaystyle \frac{30}{40} $$ $$= 0.75$$

Question 2

1 / -0

$$400$$ students of class $$X$$ of a school appeared in a test of $$100$$ marks in the subject of social
studies and the data about the marks secured is as below :

Marks secured	Number of Students
$$0-25$$	$$50$$
$$26-50$$	$$220$$
$$51-75$$	$$100$$
Above $$75$$	$$30$$
Total number of students	$$400$$

If the result card of a student he picked up at random, what is the probability that the student has secured more than $$50$$ marks.

$$0.586$$

$$0.75$$

$$0.325$$

$$0.1$$

Solution

Total number of students, i.e , the total frequency $$= 400$$
The total number of students who secured more than $$50$$ marks $$100 + 30 = 130$$
Probability that the marks secured are more than $$50 =$$ $$ \displaystyle \frac{130}{400} $$ = $$ \displaystyle \frac{1.3}{4} $$ = $$0.325$$

Question 3
1 / -0

There are $$40$$ students in a class and their results is presented as below :
Result (Pass/Fail) Pass Fail
Number of Students $$30$$ $$10$$
If a student chosen at random out of the class, find the probability that the student has passed the examination.

A
$$0.75$$

B
$$0.6$$

C
$$0.45$$

D
$$0.30$$

Solution

Total number of chances $$= 40$$
Chances or trials which favour a student to pass $$= 30$$
The probability of the required event, i.e., the student has passed the examination $$= \displaystyle \frac{30}{40} = 0.75$$
Question 4
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
$$P (H) = 0.75$$ (approx)

B
$$P (H) = 0.9$$ (approx)

C
$$P (H) = 0.15$$ (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 5
1 / -0

A die having six faces is tossed $$80$$ times and the data is as below:

Outcome

$$1$$

$$2$$

$$3$$

$$4$$

$$5$$

$$6$$

Frequency

$$10$$

$$20$$

$$10$$

$$28$$

$$8$$

$$4$$

Find $$P (1) $$.

A
$$0.175$$

B
$$0.135$$

C
$$0.145$$

D
$$0.125$$

Solution

Since, Total tosses $$=$$ $$80$$
Getting no. of $$1$$'s in total tosses $$=$$ $$10$$
$$\therefore$$ P$$(1) = \dfrac {10}{80} = 0.125 $$
Question 6
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A die is thrown $$200$$ times and the outcomes $$1, 2, 3, 4, 5, 6$$ have frequencies as below:

Outcome

$$1$$

$$2$$

$$3$$

$$4$$

$$5$$

$$6$$

Frequency

$$40$$

$$38$$

$$43$$

$$29$$

$$28$$

$$22$$

Find the probabilities of getting a number more than $$1$$ and less than $$6$$ in a toss (trial).

A
$$0.65$$

B
$$0.55$$

C
$$0.69$$

D
None of these

Solution

Since, Total cases $$= 200$$
Getting a no. more than $$1$$ and less than $$6\, (2,3,4,5) = 38+43+29+28 = 138$$
$$\therefore $$ probability $$=$$$$\dfrac {138}{200} = 0.69 $$

Question 7

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There are $$500$$ packets in a large box and each packet contains $$4$$ electronic devices in it. On testing, at the time of packing, it was noted that there are some faulty pieces in the packets. The data is as below:

No. of faulty devices in a packet	Number of packets
$$0$$	$$300$$
$$1$$	$$100$$
$$2$$	$$50$$
$$3$$	$$30$$
$$4$$	$$20$$
Total number of packets	$$500$$

If one packet is drawn from the box, what is the probability that all the four devices in the packet are without any fault?

$$0.3$$

$$0.75$$

$$0.6$$

$$0.95$$

Solution

When the packet has all the four devices without fault, it means the number of faulty devices in the packet is $$0$$.
Number of chances which are favourable to $$0$$ are $$300$$ as given in the table above. Thus, the probability of packet containing all the four devices without any fault $$=$$ $$ \displaystyle \frac{300}{500} $$ $$=$$ $$ \displaystyle \frac{3}{5} $$$$ =$$ $$0.6$$

Question 8
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In a shooting game, John shoots the balls $$20$$ times out of $$40$$ trials. What is the empirical probability of the shooting event?

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

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

C
$$\dfrac{5}{2}$$

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

Solution

The total number of trials $$= 40$$
John shoots the balls only $$20$$ times.
So, the empirical probability formula is as follows,
$$P(E) =$$ $$\dfrac{20}{40}= \dfrac{1}{2}$$
Question 9
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Directions For Questions

10 bags of wheat flour each marked 5 kg, actually contained weights of flour (in kg)
$$5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04, 5.07, 5.00$$

...view full instructions

Find probability of bag chosen out random contains more than $$5\ kg$$.

A
$$0.7$$

B
$$0.8$$

C
$$0.9$$

D
$$0.6$$

Solution

Total number of bags $$=10$$
Number of bags contain flour more than $$5kg =7$$
They are :$$5.05,5.08,5.03,5.06,5.08,5.04,5.07$$

$$P(A)=\dfrac {Number\ of\ favorable\ outcomes}{Total\ Number\ of\ possible\ outcomes} $$

$$\therefore P(A)=\dfrac{7}{10}=0.7$$
Question 10
1 / -0

What is the probability that there are $$5$$ Mondays in the month of February 2016?

A
$$0$$

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

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

D
None of the above

Solution

There are $$29$$ days in February $$2016$$.
There will be $$4$$ weeks and $$1$$ day. This one day can be any one from mon, tue, wed, thurs, fri, sat, sun.
So, probability of having $$5$$ Mondays $$=\dfrac { 1 }{ 7 } $$

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Re-Attempt Weekly Quiz Competition

Outcome	$$1$$	$$2$$	$$3$$	$$4$$	$$5$$	$$6$$
Frequency	$$10$$	$$20$$	$$10$$	$$28$$	$$8$$	$$4$$

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

Probability Test - 15

Result

Probability Test - 15

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SHARING IS CARING

Question 1

$$0.12$$

$$0.36$$

$$0.65$$

$$0.75$$

Solution

Question 2

$$0.586$$

$$0.75$$

$$0.325$$

$$0.1$$

Solution

Question 3

$$0.75$$

$$0.6$$

$$0.45$$

$$0.30$$

Solution

Question 4

$$P (H) = 0.75$$ (approx)

$$P (H) = 0.9$$ (approx)

$$P (H) = 0.15$$ (approx)

None of these

Solution

Question 5

$$0.175$$

$$0.135$$

$$0.145$$

$$0.125$$

Solution

Question 6

$$0.65$$

$$0.55$$

$$0.69$$

None of these

Solution

Question 7

$$0.3$$

$$0.75$$

$$0.6$$

$$0.95$$

Solution

Question 8

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

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

$$\dfrac{5}{2}$$

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

Solution

Question 9

$$0.7$$

$$0.8$$

$$0.9$$

$$0.6$$

Solution

Question 10

$$0$$

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

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

None of the above

Solution

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