Probability Test

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Probability Test - 13

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Question 1
1 / -0

Write the sample space when a coin is tossed.

A
S = [H, G]

B
S = [H, B]

C
S = [H, T]

D
S = [N.N)

Solution

When a coin is tossed, there are two possible outcomes: a head ($$H$$) or a tail ($$T$$). The sample space of this experiment is $$S = [H, T]$$
Question 2
1 / -0

If a card is drawn from a pack of cards. The probability of getting black ace is

A
$$\displaystyle \frac{1}{52}$$

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

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

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

Solution

Total number of cases $$= 52$$
Number of favourable cases (getting a black ace) $$= 2$$
Thus, Probability (getting a black ace) $$=$$ $$\cfrac{2}{52} = \cfrac{1}{26}$$
Question 3
1 / -0

Two dice are thrown simultaneously. Find the probability of getting an even number as the sum.

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

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

C
$$\dfrac{5}{6}$$

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

Solution

Total number of possible cases $$= 36$$
Favourable cases of getting even number as the sum
$$= \{(1, 1), (1,3), (1,5), (2, 2), (2, 4), (2, 6), (3, 1), (3, 3), (3,5), (4, 2), (4,4), (4,6), (5,1), \ \ \ \ \\ \ \ \ \ \ \ (5, 3), (5, 5), (6, 2), (6,4),\ (6, 6)\}$$
Total number of favourable cases $$= 18$$
$$P $$(getting even number as the sum) $$=$$ $$\displaystyle \frac{18}{36} = \frac{1}{2}$$
Question 4
1 / -0

If $$P(E) =0.05$$, then $$P($$not $$E) =$$

A
$$-0.05$$

B
$$0.5$$

C
$$0.9$$

D
$$0.95$$

Solution

We know that, $$0≤$$ Probability $$≤1$$
$$P(E) = 0.05$$
$$P ($$not $$E) = 1- P(E)$$
$$P($$not $$E) = 1- 0.05 = 0.95$$
Question 5
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 6
1 / -0

The probability of _____ event is 0.

A
Sure

B
Impossible

C
Exclusive

D
None of these

Solution

The probability of an impossible event is 0.
Question 7
1 / -0

Two dice are thrown simultaneously. Find the probability of getting a multiple of 2 on first dice and a multiple of 3 on the second dice.

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

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

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

D
$$\displaystyle \frac{1}{36}$$

Solution

Total cases = $$6\times 6$$
Let A be the event of getting a multiple of 2 on first dice and a multiple of 3 on the second dice.
Hence, $$A= \{(2,3),(2,6),(4,3),(4,6),(6,3),(6,6)\}$$
$$n(A) =$$ $$6$$
$$\therefore $$ $$P(A) =$$ $$ \dfrac 6{36} = \dfrac 16 $$
$$\therefore $$ Option C is correct.
Question 8
1 / -0

The probability of ____ event is 1.

A
Sure

B
Impossible

C
exclusive

D
mutually exclusive

Solution

The probability of a sure event is 1.
Question 9
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$$)=$$$$\dfrac{1}{2}$$
Question 10
1 / -0

A bag contains $$4$$ red balls, $$6$$ blue balls and $$3$$ black balls. A ball is draw at random from the bag. What is the probability that the ball drawn is not blue?

A
$$\displaystyle\frac{6}{13}$$

B
$$\displaystyle\frac{3}{13}$$

C
$$\displaystyle\frac{7}{13}$$

D
None

Solution

Total no. of balls$$=4+6+3=13$$
Total number of ways drawing one ball out of 13, n(S)$$=13C_1$$
No.of ways of drawing 1 ball,none of then is blue,n(E)$$=^{13- 6}C_1=^7C_1$$
$$\therefore probability=\dfrac{n(E)}{n(S)}=\dfrac{7}{13}$$

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Probability Test - 13

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Probability Test - 13

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Question 1

S = [H, G]

S = [H, B]

S = [H, T]

S = [N.N)

Solution

Question 2

$$\displaystyle \frac{1}{52}$$

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

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

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

Solution

Question 3

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

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

$$\dfrac{5}{6}$$

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

Solution

Question 4

$$-0.05$$

$$0.5$$

$$0.9$$

$$0.95$$

Solution

Question 5

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 6

Sure

Impossible

Exclusive

None of these

Solution

Question 7

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

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

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

$$\displaystyle \frac{1}{36}$$

Solution

Question 8

Sure

Impossible

exclusive

mutually exclusive

Solution

Question 9

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

$$1$$

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

None of these

Solution

Question 10

$$\displaystyle\frac{6}{13}$$

$$\displaystyle\frac{3}{13}$$

$$\displaystyle\frac{7}{13}$$

None

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 $$7$$