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3 years ago Edited: 3 years ago, bio_man
(4) (8-Reflecting] In a standard deck of 52 cards, your favourite card is the 9 of hearts. In a very simple game of "draw a random card from the deck" , you will be "happy" if you get a 9. You will be "happy" if you get a heart. You will be "very happy" if you get the 9 of hearts. Anything other than that will make you "sad". Make a small table showing the theoretical probability of your various possible states of happiness based on a single draw of one random card from the deck. (Show all your work) Your know-it-all friend indicates to you that the of getting a 9 are one in thirteen and the chances of getting a heart are one in four. Why aren't those numbers in your table?
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wrote...
Educator
3 years ago
Here's what I think:

Happy if:

P(pick any 9) = 4/52 = 1/13

P(pick a heart) = 12/52 = 1/4

Therefore, chances of being happy are:

(picking a heart) + (3 other 9s in deck)
(12/52) + (3/52) = 15/52

Very happy if:

P(9 of hearts) = 1/52 [only one in the whole deck]

Sad if:

P(not 9s, not hearts, and not 9 or hearts) = 1 - [ (15/52) + (1/52) ] = 9/13
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