Chat with tutor

Ask Questions, Get Answers

Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Probability

Two fair dice are tossed once. The probability of getting an even number on the first die or a total of 8 is

$\begin {array} {1 1} (1)\;\large\frac{4}{9} & \quad (2)\;\large\frac{5}{9} \\ (3)\;\large\frac{1}{3} & \quad (4)\;None\: of \: these \end {array}$


2 Answers

We have P ( even number on first die ) $ = \large\frac{1}{12}$
P ( total of 8 ) = $ \large\frac{5}{36}$
and P ( even number on first die and a total of 8 ) = $ \large\frac{1}{12}$
Using addition theorem of probability we have P ( even number on
first die or a total of 8 )
$ = \large\frac{1}{2} + \large\frac{5}{36}-\large\frac{1}{12}$
$ = \large\frac{5}{9}$
Ans : (2)


total number of outcomes are 6*6=36 condition1: let P(A) be the probability of getting an even number on the first die, first die can have 2,4,6 and 2nd die can have any of 1,2,3,4,5,6 favorable outcomes=3*6=18 therefore P(A)=18/36=1/2 condition 2: let P(B) be the probability of getting total of 8. therefore favorable outcomes={(2,6),(3,5),(4,4),(5,3),(6,2)} P(B)=5/36 now both the above cases have some cases common, i.e. when we are getting total of 8 and first die has even number. the common cases are {(2,6),(4,4),(6,2)} therefore P(A∩B)=3/36=1/12 hence the required probability: P(A∪B)=P(A)+P(B)-P(A∩B) P(even on first die or total of 8)=1/2+5/36-1/12=5/9
Help Clay6 to be free
Clay6 needs your help to survive. We have roughly 7 lakh students visiting us monthly. We want to keep our services free and improve with prompt help and advanced solutions by adding more teachers and infrastructure.

A small donation from you will help us reach that goal faster. Talk to your parents, teachers and school and spread the word about clay6. You can pay online or send a cheque.

Thanks for your support.
Please choose your payment mode to continue
Home Ask Homework Questions
Your payment for is successful.
Clay6 tutors use Telegram* chat app to help students with their questions and doubts.
Do you have the Telegram chat app installed?
Already installed Install now
*Telegram is a chat app like WhatsApp / Facebook Messenger / Skype.