# Free Probability 02 Practice Test - 10th Grade

If three coins are tossed simultaneously, then the probability of getting at least one head and tail is _____.

A. 14
B. 12
C. 34
D. 23

#### SOLUTION

Solution : C

Given, a coin is tossed 3 times.

Total possible outcomes = {HHH, HHT, HTT, HTH, THH, TTH, THT, TTT} (where H = Heads, T= Tails)
Total no. of possible outcomes = 8
Favourable outcomes (getting at least one head and tail) = {HHT, HTT, HTH, THH, TTH, THT}
No. of favorable outcomes = 6
Probability of an event E
P(E)=number of favourable outcomestotal number of outcomes

P (getting at least one head and tail)  = 6834
The probability of getting at least one head and a tail is 34.

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is black or king.

A. 12
B. 713
C. 1526
D. 813

#### SOLUTION

Solution : B

Total no. of outcomes = 52
Number of black cards (Spade+Club) in a pack of '52' cards = 26
Number of 'Kings' in a pack of cards = 4
Number of 'Black Kings' that have already been included in the number of black cards = 2
Number of favourable outcomes                           =26+42=28

Probability(getting a black or king)                       =2852=713

From a set of 17 cards, numbered 1, 2, ..., 17, one card is drawn at random. What is the  probability that number on the drawn card is a multiple of 3 or 7 ?

A.

517

B.

717

C.

817

D.

617

#### SOLUTION

Solution : B

The total number of possible outcomes(counting of the cards from 1 to 17) = 17

Favourable outcomes are 3, 6, 7, 9, 12, 14 and 15.
No. of  favourable outcomes = 7

Let E be the event of getting a multiple of 3 or 7.
Probability P(E) = Number of outcomes favorable to ENumber of all possible outcomes of the experiment=717

There are 5 green, 6 black and 7 white balls in a bag. A ball is drawn at random from the bag. Find the probability that it is not white.

A.

1118

B.

718

C.

23

D.

518

#### SOLUTION

Solution : A

Given,
Number of green balls = 5
Number of black balls = 6
Number of white balls = 7
Total number of outcomes = 5 + 6 + 7 = 18
There are 18 balls out of which 11 are not white.
Number of favourable outcomes = 11

Probability of an event, P(E)=Number of favourable outcomesTotal number of outcomes
P( ball drawn is not white) = 1118

Probability that the ball drawn is not white is 1118 .

Alternate Method:
P (ball drawn is white) = 718
By complementary event formula,
P( ball drawn is white) + P( ball drawn is not white) = 1
P( ball drawn is not white)
=1P( ball drawn is white)
=1718=1118
Probability that the ball drawn is not white is 1118.

If P(A) and P(not A) are complementary events and P(A) =  0.15, then P(not A) = ?

A.

0.35

B.

0.3

C.

0.85

D.

Cannot be determined

#### SOLUTION

Solution : C

Given, P (A) = 0.15
As, P(A) and P(not A) are complementary events, P(A) + P(not A) = 1
P (not A) = 1 – P (A) = 1 – 0.15 = 0.85

State whether the given statement is true or false:

The probability of getting a multiple of 2 in a throw of an unbiased die is 12.

A.

True

B.

False

#### SOLUTION

Solution : A

There are 3 favourable outcomes out of a total of six outcomes in this case.
Multiples of 2 6 are  2, 4, and 6.
Hence, the probability is 12

What is the probability of not picking a face card when you draw a card at random from a pack of 52 cards?

A.

113

B.

413

C.

1013

D.

1213

#### SOLUTION

Solution : C

Since there are 12 face cards in a deck of 52cards, the probability of drawing a face card is 1252=313
Hence, the probability of not picking a face card = 1313=1013

A bucket contains 10 brown balls, 8 green balls, and 12 red balls and you pick one randomly without looking. What is the probability that the ball will be brown?

A.

415

B.

13

C.

0.61

D.

0.33

#### SOLUTION

Solution : B and D

There are a total of 10 + 8 + 12 = 30 balls, out of which 10 are brown.
The required probability is 1030 = 13.

In a circular dartboard of radius 20 cm, there are 5 concentric circles. the radius of each inner concentric circle is 4 cm less than the outer concentric circle. Find the probability that a dart hits anywhere in the smallest circle assuming that the dart doesn't hit on the boundary of any circle.

A.

15

B.

125

C.

1π

D.

0

#### SOLUTION

Solution : B Difference in radius between 2 circles = 4cm

Let, radius of small circle be x.
x + 4 + 4 + 4 + 4 = 20    (from the diagram)
x = 4cm

Probability that the dart hits anywhere in the small circle  = area(innermost circle)area(outermost circle)

=π.42π202

=125

The probability of winning a game is 25, the probability of losing is__. (in decimal form)

#### SOLUTION

Solution : Winning or losing a game are complementary events. We know that, for complementary events, P(A) + P(notA) = 1.
Thus, if P(winning) = 25
Then, P(losing) = 1 - 25
P(losing) = 35 = 0.6.