appConfigEntityId

bodyType

customContents

entityId

entityUuid

articlePageQuery

filter

article

articleBaseAdvertisingInfoArticle

articleListArticle

articleSeoArticle

hooksArticleAcknowledgementGateOverlayArticle

hooksTrackPageViewArticle

hooksContentInterestArticle

articleLinkingDataContent

hooksAmpRedirectArticle

articleSchemaContent

hooksArticlePageAdvertisementConfigArticle

liveArticle

appConfig

advertZone

sentiment

contentLock

topics

types

sections

paywallTypes

createdDate

publishedDate

sponsorType

urlAlias

moreOnThisArticles

sectionsV2

commentCount

authorLocations

authors

corrections

displaySlideShow

multimediaEmbed

printHeadline

seriesContainer

articleSpeeches

socialHeadline

headline

images

flag

firstTopic

glossary

flattenTypeIds

image

relatedLinks

relatedNewsletters

__typename

sponsor

pdfFiles

seriesReverseOrder

series

disableOffPlatformContent

published

updatedDate

summary

subHeadline

body

keywords

readingTime

customTimezone

liveContents

json

SCMP Reporter

Two events are independent if the occurrence or non-occurrence of one event does not affect the probability of occurrence of the other event.

1. Two fair dice, one green and one red, are thrown.

Let A be the event that the green die is even.

Let B be the event that the red die is greater than 4.

(a) Find P (A) and P (B).

P (A) = 1/2

P (B) = 1/3

(b) Find the probability that both A and B happen.

P (green die is even and red die is greater than 4):

= 6/36   =   1/6

(c) What can you say about P (A), P (B) and P (A and B)?

If A and B are independent events, then

P (A and B)  =  P (A) P (B)

2. In tossing a coin twice, what is the probability that both are heads?

P (1st toss is H) = 1/2

P (2nd toss is H) = 1/2

P (both are H) = (1/2) (1/2)  =  1/4

3. A bag contains 3 white balls and 4 black balls. Two balls are drawn in succession from the bag. The first ball is replaced before the next one is drawn.

Let A be the event that the first ball drawn is white.

Let B be the event that the second ball drawn is black.

(a) Find P (A) and P (B)

P (A)  =  3/7

P (B)  =  4/7

(b) Find the probability that the first ball drawn is white and the second ball drawn is black.

P (A and B)  =  12/49

Product law

If E and F are independent events, then:

P (E and F)  =  P (E) P (F)

1. In a multiple-choice test, each question has five choices. If a student attempts each question by guessing, find the probability that:

(a) he will answer the first four questions correctly.

P (first four questions correct):

=  (1/5) (1/5) (1/5) (1/5)  =  1/625

(b) he will answer the first question correctly and the next

three wrongly.

P (first one correct and next three wrong):

=  (1/5) (4/5) (4/5) (4/5)

=  64/625

2. Two cards are drawn in succession from a deck of 52 cards. The first card is replaced after the first draw. Find the probability that:

(a) both are the king of spades.

P (first card is king of spades)  =  1/52

P (second card is king of spades)  =  1/52

P (both are king of spades) = (1/52)(1/52) = 1/2704

(b) the first card is a heart and the second card is the '6' of

hearts.

P (first card is a heart)  =  1/4

P (second card is the '6' of hearts) = 1/52

P (first card is a heart and the second card is the '6'

of hearts):

=   (1/4) (1/52)  =  1/208



Probability of independent events