Probability Test

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Probability Test - 17

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Weekly Quiz Competition

Question 1
1 / -0

If two coins are tossed then find the probability of the events that at the most one tail turns up

A
$$\displaystyle \frac{1}{4}$$

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

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

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

Solution

The sample space of 2 coins tossed $$= {(h,h),(h,t),(t,h),(t,t)}$$
for having atmost one tail we need$$ = (h,t),(t,h),(h,h)$$
Thus the probability is $$\cfrac{ 3}{4}$$
Question 2
1 / -0

What is number of outcomes when tossing two coins together?

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution

HT, HH, TH, TT (Here HT means Head on first coin and Tail on the second coin and so on).
so. 4 outcomes
Question 3
1 / -0

A die is thrown then find the probability of getting a perfect square.

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

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

C
$$\displaystyle \frac{2}{3}$$

D
$$0$$

Solution

Sample space $$= {1,2,3,4,5,6}$$
A perfect square in samples$$= {1,4} = 2$$
Probability of getting perfect square = $$\cfrac{2}{6}$$ =$$\cfrac{1}{3}$$
Question 4
1 / -0

If two coins are tossed then find the probability of the event that at least one tail turns up is:

A
$$\displaystyle \frac{1}{4}$$

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

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

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

Solution

2 coins tossed sample space $$= {(h,h),(h,t),(t,h),(t,t)}$$
Number of outcomes that have atleast one tail $$= 3 $$
probability is $$\cfrac{ 3}{4}$$
Question 5
1 / -0

A die is thrown then find the probability of getting a number greater than $$3$$.

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

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

C
$$\displaystyle \frac{2}{3}$$

D
$$0$$

Solution

Sample space $$={ {1,2,3,4,5,6}}$$
a no >3 in sample space$$= {4,5,6} =3$$
probability of getting no greater than =$$\cfrac{3}{6}$$ =$$\cfrac{1}{2}$$
Question 6
1 / -0

In a sample study of $$642$$ people, it was found that $$514$$ people have a high school certificate. If a person is selected at random, the probability that the person has a high school certificate is :

A
$$0.5$$

B
$$0.6$$

C
$$0.7$$

D
$$0.8$$

Solution

Given that:
Total number of people $$n(S)=642$$
No. of peoples having high school certificate $$n(E)=514$$
$$P(E)=$$Probability that the person has a school certificate
$$\therefore P(E)=\dfrac{n(E)}{n(S)}=\dfrac{514}{642}=0.8006$$
Hence, D is the correct option.
Question 7
1 / -0

A die is thrown then find the probability of getting an odd number.

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

B
$$\displaystyle \frac{2}{3}$$

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

D
None of these.

Solution

Sample space $$= {1,2,3,4,5,6}$$
odd nos. $$= 1,3,5$$
probability of getting odd nos.$$=\cfrac{3}{6}$$ $$=\cfrac{1}{2}$$
Question 8
1 / -0

In tossing a coin, the chance of throwing head and tail alternatively in $$3$$ successive trials is

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

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

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

D
$$\dfrac{1}{48}$$

Solution

Favourable outcomes $$= \{HTH,THT\}= 2$$ outcomes
Total number of outcomes $$= 8$$
Probability $$=$$ $$\dfrac{2}{8}$$ $$=$$ $$\dfrac{1}{4}$$
Question 9
1 / -0

If two coins are tossed then find the probability of the event that no head turns up.

A
$$\displaystyle \frac{1}{4}$$

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

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

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

Solution

2 coins tossed sample space $$= {(h,h),(h,t),(t,h),(t,t)}$$
have no head =$$ 1 $$(when both tail)
probability is $$\cfrac{ 1}{4}$$
Question 10
1 / -0

A box contains $$3$$ red, $$3$$ white and $$3$$ green balls. A ball is selected at random. Find the probability that the ball picked up is neither a white nor a red ball:

A
$$\displaystyle \frac{1}{4}$$

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

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

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

Solution

Total number of outcomes $$= 9$$
Favourable outcomes (the ball is neither white nor red) $$= 3$$
Probability $$=\dfrac{3}{9} = \dfrac{1}{3}$$

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Re-Attempt Weekly Quiz Competition

Probability Test - 17

Result

Probability Test - 17

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SHARING IS CARING

Question 1

$$\displaystyle \frac{1}{4}$$

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

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

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

Solution

Question 2

$$1$$

$$2$$

$$3$$

$$4$$

Solution

Question 3

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

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

$$\displaystyle \frac{2}{3}$$

$$0$$

Solution

Question 4

$$\displaystyle \frac{1}{4}$$

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

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

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

Solution

Question 5

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

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

$$\displaystyle \frac{2}{3}$$

$$0$$

Solution

Question 6

$$0.5$$

$$0.6$$

$$0.7$$

$$0.8$$

Solution

Question 7

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

$$\displaystyle \frac{2}{3}$$

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

None of these.

Solution

Question 8

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

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

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

$$\dfrac{1}{48}$$

Solution

Question 9

$$\displaystyle \frac{1}{4}$$

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

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

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

Solution

Question 10

$$\displaystyle \frac{1}{4}$$

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

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

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

Solution

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