Steemkids Mathematics Lesson Week 12||Addition and Multiplication laws of Probability

2개월 전

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Introduction

Good morning my dear friends.Here is another week of unlimited opportunities and new time to learn something new.Just like wonders, learning never end.I am sure we are educating each other through this lesson.Welcome to the 12th week of our lesson series for this season.

As part of contributing to the #learnwithsteem and #lesson initiative which is geared towards the growth of Steem across the countries of the world,I am delighted to continue presenting this lesson series every fortnight.

Never forget that the main aim of this lesson series is to improve our mathematics solving skills,learn more about mathematics,foster engagement among participants and sharing of ideas.

PROBABILITY

We are still continuing with the topic probability- because the topic is too vast and we have to take it step by step.We shall mainly look at addition and multiplication laws of probability. Remember that probability- is the likelihood or chances of an event happening.Mathematically, probability is simply dividing the required outcome by the total outcome.👇

Probability=required outcome/total outcome

Salient Points in Addition and Multiplication laws of Probability

  • For the addition law to be applied,the question must have any of these key words:either, neither, or. Whenever,you see them,it means that you should perform addition (adding together).

  • For the multiplication law to be applied,the question must have any of these key words:both, and,all. Whenever,you see them,it means that you should perform multiplication.

  • If the probability that an event will happen is 2/3.Then,for that event not to happen again is 1 - (2/3).

Practical Problems

Pls refer to this my video to see a visual solution to the first question.👇

1.)A bag contains 4 red balls,3 white balls and 5 green balls.If a ball is picked at random,what is the probability that it
a.)red or green b.)green or white c.)not green

Solution:

Remember that or means addition(+).

Total outcome=red + white + green
Total outcome=4+3+5=12

Probability=required outcome divided by total outcome.
a.) Probability of red or green=4/12+5/12=9/12=3/4

b.) Probability of green or white=5/12+3/12=8/12=2/3.

c.) Probability of NOT green=1 - (probability of green)
=1 - 5/12=1/1 - 5/12=7/12


2.)A bag contains 6 black balls and 4 white balls.Two balls are picked 'with replacement'.What is the probability that:
a.)both are black b.)both are white c.)both are same colour

Solution:

Remember that both means multiplication(×).

Total outcome=black + white
Total outcome=6+4=10

Probability=required outcome divided by total outcome.

a.) Probability that both are black=6/10 x 6/10=36/100=9/25

b.) Probability that both are white =4/10 x 4/10=16/100=4/25

c.) Probability that both are same colour.
This statement never mentioned the colour,so it means that both can be black or both can be white.

Probability that both are same colour=(6/10 x 6/10) Or (4/10 x 4/10)

=(6/10 x 6/10) + (4/10 x 4/10)

=(9/25) + (4/25)=13/25

NB:This question involves with replacement,there are some that involves without replacement - and in such case,the total outcome reduces by one after the first picking.

Homework

1.)A bag contains 7 black balls and 3 red balls.Two balls are picked 'with replacement'.What is the probability that:
a.)both are black b.)both are red c.)both are same colour

2.)A bag contains 5 red balls,2 white balls and 3 green balls.If a ball is picked at random,what is the probability that it:
a.)red or green b.)green or white c.)not green

RULES/TERMS

•The deadline for the submisson of the homework is 11:59pm on Saturday.

•Only the verified kids account would be used for the homework.

•This homework is strictly for the kids.Adults can only help to take a picture of the work for them.

•I would love if username is written on each answer to avoid plagiarism.

•Drop your answers (pictures) as a comment under the comment section of this post(compulsory).

I am inviting @chimeroselam @richy20 @graceani
@shulamite10, @geoscary, @nataliugo, @garyson7, @wizzyboy3, @fortwis09, @chukwu10, @favour11,@whakee @princeifeko to participate

Written by:@samuel20
For:@steemkids

Cc:@ngoenyi

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Beautiful lesson!

Here is my entry

Homework

  • A bag contains 7 black balls and 3 red balls.Two balls are picked 'with replacement'.What is the probability that:

a.)both are black
ANS: Total outcome =7+3
=10
Multiplication of both black balls =
7/10 × 7/10
=49/100//

b.)both are red
ANS:
= 3/10× 3/10
=9/100//

c.)both are same colour
ANS:
For both to be same colour, therefore,
(49/100) + (9/100)
IMG_20220726_231743_071.jpg
29/50//

20220518_060409.jpg

  • A bag contains 5 red balls,2 white balls and 3 green balls.If a ball is picked at random,what is the probability that it:

a.)red or green
ANS:
OR means addition
Total outcome: 5+2+3=10
Red or green =
5/10+3/10
=8/20
=2/5//

b.)green or white
=3/10+2/10
=5/20
=1/4//

c.)not green
= 1-3/10
= 1/1-3/10

IMG_20220726_233831_827.jpg
=7/10//