Email
Chat with tutor
logo

Ask Questions, Get Answers

X
 
Questions  >>  CBSE XII  >>  Math  >>  Probability
Answer
Comment
Share
Q)

One card is drawn at random from a well shuffled deck of 52 cards. Are E and F independent if E : the card drawn is a king or queen F : the card drawn is a queen or jack?

This is a multi part question answered separately on Clay6.com

1 Answer

Comment
A)
Toolbox:
  • If A and B are independent events, \(P(A\cap\;B)=P(A)\;P(B)\)
Given a deck of 52 cards, there are 4 kings, 4 queens and 4 jacks, and the P(drawing a king) = P(drawin a queen) = P(drawing a jack) = $\large\frac{4}{52} = \frac{1}{13}$
Given E: the card drawn is a king or queen, P (E) = P(king) + P(queen) = $\large\frac{1}{13} + \frac{1}{13} = \frac{2}{13}$
Given F: the card drawn is a queen or a jack, P(F) = P(queen) + P(jack) = = $\large\frac{1}{13} + \frac{1}{13} = \frac{2}{13}$
If A and B are independent events, \(P(A\cap\;B)=P(A)\;P(B)\)
P (E $\cap F) = P (card drawn is a queen) = $\large\frac{4}{52} = \frac{1}{13}$
P (E $\cap$ F) = P(E) $\times$ P(F) = $\large\frac{2}{13}$$\;\times$$\large\frac{2}{13} = \frac{4}{169} $$\;\neq \large\frac{1}{13}$
Therefore E and F are NOT independent
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.
Continue
Please choose your payment mode to continue
Home Ask Homework Questions
Your payment for is successful.
Continue
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.
...