SOLUTION: If one card is drawn from a deck, find the probability of getting the following result:
A 6 or a spade
hearts: (1/52)
clubs: (1/52)
spades: (13/52) 6 is also included
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Question 1049992: If one card is drawn from a deck, find the probability of getting the following result:
A 6 or a spade
hearts: (1/52)
clubs: (1/52)
spades: (13/52) 6 is also included in the spades suite
diamonds: (1/52)
This totals 16 cards.
P of getting a 6 (1/52) + (1/52) + (1/52) = (3/52)
P of getting a spade = (13/52)
(3/52) + (13/52) = 16/52 = 4/13
Is this answer correct? Is it correct to reduce 16/52 to 4/13?
I understand that 6 is included in the spades suite so I just excluded the 4th 1/52 for 6 but somehow I feel like I should have included this 1/52
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you want the probabililty of getting a 6 or a spade.
the probability of getting a 6 is 4/52.
the probability of getting a spade is 13/52.
the probability of getting a 6 and a spade at the same time is 1/52.
that would be the 6 of spades.
p(a or b) = p(a) + p(b) - p(a and b).
you get p(a or b) = 4/52 + 13/52 - 1/52.
this becomes p (a or b) = 16/52 which can be simplified to 4/13.
this looks like the answer you arrived at without using the formula i showed you above.
let's look at what you did.
you did:
If one card is drawn from a deck, find the probability of getting the following result:
A 6 or a spade
hearts: (1/52) ***** you mean one 6 of hearts i presume.
clubs: (1/52) ***** you mean one 6 of clubs i presume.
spades: (13/52) 6 is also included in the spades suite ***** correct.
diamonds: (1/52) ***** you mean one 6 of diamonds i presume.
This totals 16 cards ***** correct.
P of getting a 6 = (1/52) + (1/52) + (1/52) = (3/52) ***** correct - this does not include the 6 of spades.
P of getting a spade = (13/52) ***** correct - this includes the 6 of spades.
(3/52) + (13/52) = 16/52 = 4/13 ***** correct -it's ok to simplify the fraction.
your approach was logical and correct even though you didn't use the formula shown above.
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