GCSE Edexcel Maths The Circle: Marek has 9 cards. There is a nu

Marek has 9 cards - Edexcel - GCSE Maths - Question 17 - 2019 - Paper 2

Question 17

Marek has 9 cards. There is a number on each card. 1 2 3 4 5 6 7 8 9 Marek takes at random two of the cards. He works out the product of the numbers on the two car... show full transcript

Worked Solution & Example Answer:Marek has 9 cards - Edexcel - GCSE Maths - Question 17 - 2019 - Paper 2

Step 1

Step 1: Identify Cases for Even Product

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Answer

To find the probability that the product of two selected numbers is even, we need to first determine how the product can result in an even number. A product is even if at least one of the selected numbers is even. In our case, the even numbers from the cards are 2, 4, 6, and 8.

Step 2

Step 2: Calculate Total Combinations of Cards

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Answer

The total ways to select 2 cards from 9 is given by the combination formula:

$C(9, 2) = \frac{9!}{2!(9-2)!} = \frac{9 \times 8}{2 \times 1} = 36$

Step 3

Step 3: Calculate Combinations Leading to Even Product

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The only scenario where the product is odd is when both numbers chosen are odd. The odd numbers available are 1, 3, 5, 7, and 9, totaling 5 odd numbers. The number of ways to choose 2 odd numbers is:

$C(5, 2) = \frac{5!}{2!(5-2)!} = \frac{5 \times 4}{2 \times 1} = 10$

Thus, the number of combinations that result in an even product is:

$36 - 10 = 26$

Step 4

Step 4: Calculate Probability of Even Product

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The probability that the product is even can then be calculated as follows:

$P(Even) = \frac{Number \ of \ Even \ Combinations}{Total \ Combinations} = \frac{26}{36} = \frac{13}{18}$

Marek has 9 cards - Edexcel - GCSE Maths - Question 17 - 2019 - Paper 2

Worked Solution & Example Answer:Marek has 9 cards - Edexcel - GCSE Maths - Question 17 - 2019 - Paper 2

Step 1: Identify Cases for Even Product

Step 2: Calculate Total Combinations of Cards

Step 3: Calculate Combinations Leading to Even Product

Step 4: Calculate Probability of Even Product

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