PROBABILITY ( LECTURE 2)

LESSON 2 PROBABILITY

DEAR STUDENTS
WELCOME TO THE CLASS  !!

We will start our class today with an AQAD(Note down in the notebook)

Let us go through the guidelines for the  blog once again:

•              The text in Red, is to be writtenin your register

•              The text in blue is to be viewedby clicking on it

•              The text in green is to be practiced for home work

General Instructions

•               take your Mathematics Register

Write down Today's learning outcomes:

I will be able to:

1. recall basic definitions  related to probability.

2.    comprehend and memorize the scheme of cards

3. calculate probability related to playing cards.

Yesterday you all learnt about various terms and types of events

 Today we will learn more.....

Click on the link

Now, note down

The probability  of an event E, written as P(E), is defined as
P(E) = Number of outcomes favourable to E      

            Number of all possible outcomes of the experiment

0  ≤  P(E) ≤ 1

That is, the probability of an event which is impossible to occur is 0. Such an event is called an impossible event.

EG.getting 8 in a single throw of a die

the probability of an event which is sure (or certain) to occur is 1. Such an event is called a sure event or a certain event.

EG  getting a number less than 7 

in a single throw of a die

COMPLEMENTARY EVENTS

For an event E,

 Have you seen a deck of playing cards? 

Look at the scheme of cards in the image below.

CLICK ON THE LINK TO GET MORE CLARITY

All to note ↔☟:

.KINGS.QUEENS AND JACKS ARE CALLED "FACE CARDS" total (4+4+4=12 )in number.

You all have been through the link above. Did you notice a question at the end of it?

The question was: A card was drawn from a well shuffled deck of cards,what  is the probability of getting a king of red colour?(make a note)

Why do we take a well shuffled pack of cards?

Ans: Well-shuffling ensures equally likely outcomes.

Let's try to solve the question

How many red cards are there in a pack of cards?

26 out of 52

What is the probability of getting a red card?

=26/52=1/2

How many kings are there in a pack of cards?

4 out of 52

What is the probability of getting a king?

=4/52=1/13

How many kings are of red colour in a pack of cards  ?

2  out of 52

What is the probability of getting a king of red colour?

=2/52 =1/26

Example 4 : One card is drawn from a well-shuffled deck of 52 cards. Calculate the probability that the card will
(i) be an ace,
(ii) not be an ace.
Solution :
(i) There are 4 aces in a deck. .
The number of favourable outcomes   = 4
The number of possible outcomes = 52
Therefore, P(getting an ace) = 4/52

=1/13
  (ii) The number of  favourable outcomes   = 52 – 4 = 48 (remove  4 aces from 52 cards)

so,P(not getting an ace)= 48/52

= 12/13

OR

P(not getting an ace) = 1- P(getting an ace)  (complementary events)

=1 -1/13

=12/13

let's do Q15 OF EX 15.1

NOW,YOU CAN ATTEMPT Q14 OF EX15.1 AS HW

LET'S PRACTICE SOME MORE  QUESTIONS↱☟

Q1

CLICK ON THE LINK 

Have you gone through the solution in the above link?

Now, complete  the solution.

i) 

Total  Spades  $=\dots 13\dots ..$

Total Aces $=\dots \dots ..4.$

Number of Aces of 'Spade' $=1$

Therefore, 

Probability of the card drawn is a card of spade or an Ace:

$\frac{13}{52}+\frac{4}{52}-\frac{1}{52}$

$(card\; can\; be\; either\; spade\; or\; ace\; not\; both\; ,so\; we\; have\; to\; remove\; 1\; ace\; of\; \text{'}spade\text{'})$

$\frac{16}{52}=\frac{4}{13}$

(ii) 

Total black kings: ……..

Probability of the card drawn is a black king:

$\frac{...}{52}=\frac{}{26}$

(iii) Probability of the card drawn is neither a jack nor a king

Total jacks $=4$

Total Kings $=4$

Probability of the card drawn is neither a jack nor a king:

1- P(either jack or king)   

$1-(\frac{4+4}{52})=\frac{}{13}$

(iv) 

Total Queens $=\dots ...$

Total Kings $=\dots ...$

Probability of the card drawn is either a king or a queen:

P(King) + P(queen)   (why we didn't subtract anything here as in part (i)?)

$\frac{4+4}{52}=\frac{2}{13}$

​

HW☟

Q2 One card is drawn from the well shuffled pack of 52 cards. Find the probability of getting a black face card.

Q3.A card is drawn at random from a deck of playing cards. Find the probability of getting  not a face card.

Q4 The king, queen and jack of diamonds are removed from a pack of 52 playing cards and the pack is well shuffled. A card is drawn from the remaining cards. Find the probability of getting a card of   (i) diamond (ii) a jack

Q5Red kings, queens and jacks are removed from a deck of 52 playing cards and then well-shuffled. A card is drawn from the remaining  cards. Find the probability of getting (i) King (ii) a red card (iii) a spade

let's go through the SDG -6 

That's all  for today!!
See you tomorrow for the next class!!