UNIT V
PROBABILITY
Probability:
A probability is a number that represents the chance or likelihood that a
specific event will take place.
Formula:
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑣𝑜𝑢𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒
Probability of an event occurring =
𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒
Concepts:
∙ If the term “or” appears in a question, use addition (+) when
applying the Fundamental Principle of Counting.
∙ If the term “and” appears in a question, use multiplication (×) when
applying the Fundamental Principle of Counting.
∙ Number of Outcomes for Rolling Dice = 6 n , where n is the number of
dice rolled at once:
✔ For 1 die, the outcomes are 61 = 6.
✔ For 2 dice, the outcomes are 62 = 36.
✔ For 3 dice, the outcomes are63 = 216.
∙ Number of Outcomes for Tossing Coins = 2 n , where n is the number of
coins tossed at once:
✔ For 1 coin, the outcomes are 21 = 2.
✔ For 2 coins, the outcomes are 22 = 4.
✔ For 3 coins, the outcomes are 23 = 8.
∙ Number of Outcomes for Drawing a Card = 52 n , where n is the number
of sets or decks of cards used:
✔ For 1 deck of cards, the outcomes are 521 = 52.
✔ For 2 decks of cards, the outcomes are 522 = 2,704.
✔ For 3 decks of cards, the outcomes are 523 = 1,40,6085.
𝟑×𝟐
Formula : 𝟑𝑪𝟐 =
𝟐×𝟏
COIN BASED
1. In a toss of a single coin,
i) Find the probability of tail?
ii) Find the probability of head?
2. In a simultaneous toss of 2 coins then,
i) Find the probability of 2 heads?
ii) Find the probability of exactly one tail?
,iii) What is the probability of getting at least one tail?
iv) What is the probability of getting at most one tail?
v) Find the probability that there is no tail?
3. In a simultaneous toss of 3 coins,
i) Find the probability of all are heads?
ii) What is the probability of getting at most two heads?
iii) What is the probability of getting at least two tails?
iv) What is the probability of getting exactly 2 heads?
v) Find the probability of getting at least 1 head and 1 tail?
DICES BASED
1. In a single throw of one dice,
i) Find the probability of getting a total of 2 or 4?
ii) What is the probability of getting an even number when a
dice is rolled? iii) Find the probability of getting a multiple of 3.
2. A man throws two dice simultaneously on the floor,
i) What is the probability of getting two numbers whose
product iseven?
ii) What is the probability that the total score is a prime
number?
iii) In a single throw of two dice, find the probability that neither a doublet
nor a total of 8 will appear?
iv) What is the probability of getting two numbers whose product is
even?
v) In a simultaneous throw of two dice, what is the probability of
getting a doublet?
vi) Two dice are rolled simultaneously. Find the probability of getting the sum
of numbers on the on the two faces divisible by 3 or 4?
3. A man tossed three dice,
i) What is the probability of getting a sum 5 from two throws
, of a dice? ii) What is the probability of getting sum are 7?
iii) Three dice are thrown simultaneously. Find the probability that all of them
show the same face?
iv) What is the probability of getting at least one six in a single throw?
CARDS BASED
1. One card is drawned random from the well shuffled pack of 52 cards.
What is the probability of picking a black card?
2. A card is drawn from a pack of 52 cards. The probability of getting a
queen of club or a King of heart is?
3. One card is drawn at random from a pack of 52 cards. What is the probability
that the card drawn is a face card (Jack, Queen and King only)?
4. From a pack of 52 cards, two cards are drawn together at random. What is
the probability of both the cards being kings?
5. Two cards are drawn together from a pack of 52 cards. The probability that
one is a spade and one is a heart, is:
6. Two cards are drawn at random from a pack of 52 cards. What is the
probability that either both are black or both are queen?
7. What is the probability of getting ace of spades or the jack
ofdiamonds?
BALL BASED
1. A box contains 2 red, 3 green, and 2 blue balls. What is the probability
that none of the balls drawn is blue?
2. In a bag, there are 8 red, 7 yellow and 6 green balls. If one ball is picked
up at random, what is the probability that it is neither red nor green?
3. A box contains 4 white, 5 red, and 6 blue balls. If three balls are drawn at
random from the box, what is the probability that all of them are blue?
4. A bag contains 6 white and 4 black balls .2 balls are drawn at random. Find
the probability that they are of same colour.
5. A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at
random from the bag. The probability that all of them are red, is:
6. In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up
randomly. What is the probability that it is neither red nor green?
7. An bag contains 4 white 6 black and 8 red balls. If 3 balls are drawn one by
one without replacement, find the probability of getting all white balls?
PROBABILITY
Probability:
A probability is a number that represents the chance or likelihood that a
specific event will take place.
Formula:
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑣𝑜𝑢𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒
Probability of an event occurring =
𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒
Concepts:
∙ If the term “or” appears in a question, use addition (+) when
applying the Fundamental Principle of Counting.
∙ If the term “and” appears in a question, use multiplication (×) when
applying the Fundamental Principle of Counting.
∙ Number of Outcomes for Rolling Dice = 6 n , where n is the number of
dice rolled at once:
✔ For 1 die, the outcomes are 61 = 6.
✔ For 2 dice, the outcomes are 62 = 36.
✔ For 3 dice, the outcomes are63 = 216.
∙ Number of Outcomes for Tossing Coins = 2 n , where n is the number of
coins tossed at once:
✔ For 1 coin, the outcomes are 21 = 2.
✔ For 2 coins, the outcomes are 22 = 4.
✔ For 3 coins, the outcomes are 23 = 8.
∙ Number of Outcomes for Drawing a Card = 52 n , where n is the number
of sets or decks of cards used:
✔ For 1 deck of cards, the outcomes are 521 = 52.
✔ For 2 decks of cards, the outcomes are 522 = 2,704.
✔ For 3 decks of cards, the outcomes are 523 = 1,40,6085.
𝟑×𝟐
Formula : 𝟑𝑪𝟐 =
𝟐×𝟏
COIN BASED
1. In a toss of a single coin,
i) Find the probability of tail?
ii) Find the probability of head?
2. In a simultaneous toss of 2 coins then,
i) Find the probability of 2 heads?
ii) Find the probability of exactly one tail?
,iii) What is the probability of getting at least one tail?
iv) What is the probability of getting at most one tail?
v) Find the probability that there is no tail?
3. In a simultaneous toss of 3 coins,
i) Find the probability of all are heads?
ii) What is the probability of getting at most two heads?
iii) What is the probability of getting at least two tails?
iv) What is the probability of getting exactly 2 heads?
v) Find the probability of getting at least 1 head and 1 tail?
DICES BASED
1. In a single throw of one dice,
i) Find the probability of getting a total of 2 or 4?
ii) What is the probability of getting an even number when a
dice is rolled? iii) Find the probability of getting a multiple of 3.
2. A man throws two dice simultaneously on the floor,
i) What is the probability of getting two numbers whose
product iseven?
ii) What is the probability that the total score is a prime
number?
iii) In a single throw of two dice, find the probability that neither a doublet
nor a total of 8 will appear?
iv) What is the probability of getting two numbers whose product is
even?
v) In a simultaneous throw of two dice, what is the probability of
getting a doublet?
vi) Two dice are rolled simultaneously. Find the probability of getting the sum
of numbers on the on the two faces divisible by 3 or 4?
3. A man tossed three dice,
i) What is the probability of getting a sum 5 from two throws
, of a dice? ii) What is the probability of getting sum are 7?
iii) Three dice are thrown simultaneously. Find the probability that all of them
show the same face?
iv) What is the probability of getting at least one six in a single throw?
CARDS BASED
1. One card is drawned random from the well shuffled pack of 52 cards.
What is the probability of picking a black card?
2. A card is drawn from a pack of 52 cards. The probability of getting a
queen of club or a King of heart is?
3. One card is drawn at random from a pack of 52 cards. What is the probability
that the card drawn is a face card (Jack, Queen and King only)?
4. From a pack of 52 cards, two cards are drawn together at random. What is
the probability of both the cards being kings?
5. Two cards are drawn together from a pack of 52 cards. The probability that
one is a spade and one is a heart, is:
6. Two cards are drawn at random from a pack of 52 cards. What is the
probability that either both are black or both are queen?
7. What is the probability of getting ace of spades or the jack
ofdiamonds?
BALL BASED
1. A box contains 2 red, 3 green, and 2 blue balls. What is the probability
that none of the balls drawn is blue?
2. In a bag, there are 8 red, 7 yellow and 6 green balls. If one ball is picked
up at random, what is the probability that it is neither red nor green?
3. A box contains 4 white, 5 red, and 6 blue balls. If three balls are drawn at
random from the box, what is the probability that all of them are blue?
4. A bag contains 6 white and 4 black balls .2 balls are drawn at random. Find
the probability that they are of same colour.
5. A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at
random from the bag. The probability that all of them are red, is:
6. In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up
randomly. What is the probability that it is neither red nor green?
7. An bag contains 4 white 6 black and 8 red balls. If 3 balls are drawn one by
one without replacement, find the probability of getting all white balls?
