Probability Test

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Probability Test - 19

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Weekly Quiz Competition

Question 1
1 / -0

One coin is tossed once. Find the probability of getting A tail.

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

B
$$1$$

C
Data insufficient

D
None of these

Solution

There are $$2$$ possible outcomes of a throw of coin.
$$P($$tail$$)=$$$$\dfrac{1}{2}$$
Question 2
1 / -0

Two unbiased coins are tossed simultaneously. Find the probability of getting at most one head.

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

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

C
$$\dfrac{3}{4}$$

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

Solution

Since, Total possibilities are $$=$$ $$\{HH,HT,TH,TT\}$$
no. of cases with atmost one head are $$= \{HT,TH,TT\}$$
$$\therefore $$ probability = $$\dfrac {3}{4} $$
Option C is correct.
Question 3
1 / -0

An unbiased die is thrown. The probability of getting a number between $$1$$ and $$6$$ is

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

B
$$ \displaystyle \frac{2}{6} $$

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

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

Solution

Total number of outcomes ={1,2,3,4,5,6}
Favourable outcomes = {2,3,4,5}
Probability $$=\dfrac{4}{6} = \dfrac{2}{3}$$
Question 4
1 / -0

One card is drawn from a pack of $$52$$ cards.The probability of getting a $$10$$ of black suit is

A
$$ \displaystyle \frac{1}{26} $$

B
$$ \displaystyle \frac{1}{13} $$

C
$$ \displaystyle \frac{3}{26} $$

D
None

Solution

Favourable number of outcomes, with $$10$$ of black suit $$= 2$$
Total number of outcomes $$= 52$$
Thus, probability $$=\dfrac{2}{52} =\dfrac{1}{26}$$
Question 5
1 / -0

Two unbiased coins are tossed simultaneously. The probability of getting two heads

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

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

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

D
None

Solution

Favourable number of outcomes, getting two heads = $$1$$ i.e {HH}
Total number of outcomes =$$6$$ i.e {HH, HT, TH, TT}
Probability $$=\dfrac{1}{4}$$
Question 6
1 / -0

A die is thrown. The probability of getting an odd number is

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

B
$$ \displaystyle \frac{2}{6} $$

C
$$ \displaystyle \frac{4}{6} $$

D
None

Solution

Total number of outcomes = {1,2,3,4,5,6}
Favourable outcomes= {1,3,5}
Probability $$=\dfrac{3}{6} = \dfrac{1}{2}$$
Question 7
1 / -0

There are $$50$$ students in a class and their results is below:

Result (Pass/Fail)

Pass

Fail

No. of students

$$35$$

$$15$$

If a student chosen at random out of the class (i.e., without any bias), find the probability that the student is not failing (i.e., the student passed the examination).

A
$$0.7$$

B
$$0.66$$

C
$$0.9$$

D
$$1$$

Solution

Total number of students $$= 50$$
Number of students passed $$= 35$$
Probability, student is not failed $$=$$ probability that student is passed $$= \dfrac{35}{50} = 0.7$$
Question 8
1 / -0

When a die is thrown, list the outcomes of an event of getting:
I. A prime number,
II. Not a prime number.

A
Prime number are $$2,3$$ and $$5$$
Not a prime number are $$1, 4$$ and $$6$$

B
Prime number are $$2,7$$ and $$9$$
Not a prime number are $$1, 4$$ and $$6$$

C
Prime number are $$2,3$$ and $$5$$
Not a prime number are $$1, 5$$ and $$7$$

D
None of these

Solution

In a throw of die, the total outcomes are $$\{1,2,3,4,5,6\}$$
(a) A prime number are $$2,3$$ and $$5$$.
(b) Not a prime number are $$1, 4$$ and $$6$$.
Hence the answer is option A
Question 9
1 / -0

In a simultaneous throw of two dice what is the probability of getting a doublet ?

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

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

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

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

Solution

Total number of possibilities = $$36$$
Number of doublet = $$6$$
Thus, probability = $$\dfrac{6}{36} = \dfrac{1}{6}$$
Question 10
1 / -0

One coin is tossed once. Find the probability of getting A head.

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

B
$$1$$

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

D
None of these

Solution

The outcome of a throw of coin can be $$2$$.
$$P($$head$$)=$$$$\dfrac{1}{2}$$

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Probability Test - 19

Result

Probability Test - 19

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SHARING IS CARING

Question 1

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

$$1$$

Data insufficient

None of these

Solution

Question 2

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

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

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

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

Solution

Question 3

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

$$ \displaystyle \frac{2}{6} $$

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

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

Solution

Question 4

$$ \displaystyle \frac{1}{26} $$

$$ \displaystyle \frac{1}{13} $$

$$ \displaystyle \frac{3}{26} $$

None

Solution

Question 5

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

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

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

None

Solution

Question 6

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

$$ \displaystyle \frac{2}{6} $$

$$ \displaystyle \frac{4}{6} $$

None

Solution

Question 7

$$0.7$$

$$0.66$$

$$0.9$$

$$1$$

Solution

Question 8

Prime number are $$2,3$$ and $$5$$Not a prime number are $$1, 4$$ and $$6$$

Prime number are $$2,7$$ and $$9$$Not a prime number are $$1, 4$$ and $$6$$

Prime number are $$2,3$$ and $$5$$Not a prime number are $$1, 5$$ and $$7$$

None of these

Solution

Question 9

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

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

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

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

Solution

Question 10

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

$$1$$

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

None of these

Solution

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Prime number are $$2,3$$ and $$5$$
Not a prime number are $$1, 4$$ and $$6$$

Prime number are $$2,7$$ and $$9$$
Not a prime number are $$1, 4$$ and $$6$$

Prime number are $$2,3$$ and $$5$$
Not a prime number are $$1, 5$$ and $$7$$