In: Statistics and Probability
Your friend picks a random card and wants you to guess if it’s a face card. He tells you that it’s red. He tells you that is not a 10. He tells you that it’s not a diamond. Which of these are independant and which are dependant?
Out of 52 cards, there are 26 red cards ,6 of which are face cards and out of 52 cards , in total 12 face cards
therefore probability that it is a face card knowing that the card is red (6/26=0.23) is not different from probability that it is a face card not knowing about the color (12/52=0.23). Therefore independent event
Out of 52 cards, there are 4 ten cards , so there are 48 cards are there that are not 10
therefore probability that it is a face card knowing that the card is not 10 (12/48) is different from probability that it is a face card not knowing anything (12/52). Therefore dependent event
Out of 52 cards, there are 13 diamond cards , so there are 39 cards are there that are not diamond , 9 face cards are not diamond
therefore probability that it is a face card knowing that the card is not diamond (9/39=0.23) is not different from probability that it is a face card not knowing anything (12/52=0.23). Therefore independent event