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# Paul has 8 cards. [GCSE MATHS PAST PAPER QUESTION]

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1. I see the community here is cool so i thought i'd ask a question:

Paul has 8 cards.
There is a number on each card.

2,3,3,4,5,5,5,5

Paul takes at random 3 cards.
He adds together the 3 numbers on the card to get a total T

Work out the probability that T is an odd number.

2. (Original post by Kasperov)
I see the community here is cool so i thought i'd ask a question:

Paul has 8 cards.
There is a number on each card.

2,3,3,4,5,5,5,5

Paul takes at random 3 cards.
He adds together the 3 numbers on the card to get a total T

Work out the probability that T is an odd number.

There are two cards with even numbers and six cards with odd numbers. For the sum to be odd Paul must have two even and one odd card at any time or have all three cards that have odd numbers. This could happen in the following combinations:

Odd even even
even odd even
even even odd
odd odd odd

The probability of each combination is shown below:

odd even even = (6/8) x (2/7) x (1/6) = 1/28
even odd even = (2/8) x (6/7) x (1/6) = 1/28
even even odd = (2/8) x (1/7) x (6/6) = 1/28
odd odd odd = (6/8) x (5/7) x (4/6) =5/14
now add all of these probabilities together : 1/28 +1/28 + 1/28 + 5/14 =13/28

Hope that helps
3. odd,odd,even
even,odd,odd
odd,even,odd

1- p(even possibilities) = odd values
1- 3(6/8 x 5/7 x 2/6)
1-3(60/336)
1-(180/336) = 156/336 = 13/28
4. (Original post by anujsr)
There are two cards with even numbers and six cards with odd numbers. For the sum to be odd Paul must have two even and one odd card at any time or have all three cards that have odd numbers. This could happen in the following combinations:

Odd even even
even odd even
even even odd
odd odd odd

The probability of each combination is shown below:

odd even even = (6/8) x (2/7) x (1/6) = 1/28
even odd even = (2/8) x (6/7) x (1/6) = 1/28
even even odd = (2/8) x (1/7) x (6/6) = 1/28
odd odd odd = (6/8) x (5/7) x (4/6) =5/14
now add all of these probabilities together : 1/28 +1/28 + 1/28 + 5/14 =13/28

Hope that helps
odd,odd,even
even,odd,odd
odd,even,odd

1- p(even possibilities) = odd values
1- 3(6/8 x 5/7 x 2/6)
1-3(60/336)
1-(180/336) = 156/336 = 13/28
Thanks guys

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