# Free Probability 02 Practice Test - 10th Grade

### Question 1

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

#### 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) = 68 = 34

∴ The probability of getting at least one head and a tail is 34.

### Question 2

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

#### 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+4−2=28

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

### Question 3

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 ?

517

717

817

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

### Question 4

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.

1118

718

23

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)

=1−P( ball drawn is white)

=1−718=1118

∴ Probability that the ball drawn is not white is 1118.

### Question 5

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

0.35

0.3

0.85

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

### Question 6

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.

True

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.

### Question 7

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

113

413

1013

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 = 1−313=1013

### Question 8

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?

415

13

0.61

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.

### Question 9

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.

15

125

1π

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 = 4cmProbability that the dart hits anywhere in the small circle = area(innermost circle)area(outermost circle)

=π.42π202

=125

### Question 10

The probability of winning a game is 25, the probability of losing is

#### 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.