Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XII  >>  Math  >>  Probability
0 votes

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 black F : the card drawn is a king?

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

Can you answer this question?

1 Answer

0 votes
  • If A and B are independent events, \(P(A\cap\;B)=P(A)\;P(B)\)
In a deck there are 52 cards - 26 of each color and and there are 4 kings, one in each suit, and 2 of each color.
Given E: the card drawn is black, P(E) = $\large\frac{26}{52} = \frac{1}{2}$
Given F: the card drawn is a king, P(F) = $\large\frac{4}{52} = \frac{1}{13}$
If A and B are independent events, \(P(A\cap\;B)=P(A)\;P(B)\)
P (black card $\cap$ king ) = P (E $\cap$ F) = P (drawing an black king) = $\large\frac{2}{52} = \frac{1}{26}$
Now, P (E $\cap$ F) = P(E) $\times$ P(F) = $\large\frac{1}{2}$$\;\times$$\large\frac{1}{13} = \frac{1}{26}$
Therefore E and F are independent
answered Jun 19, 2013 by balaji.thirumalai

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App