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Three squares are chosen at random from the 3 × 3 grid below, and a cross is placed in each chosen square - HSC - SSCE Mathematics Extension 1 - Question 10 - 2017 - Paper 1
Question 10
Three squares are chosen at random from the 3 × 3 grid below, and a cross is placed in each chosen square. What is the probability that all three crosses lie in the... show full transcript
Worked Solution & Example Answer:Three squares are chosen at random from the 3 × 3 grid below, and a cross is placed in each chosen square - HSC - SSCE Mathematics Extension 1 - Question 10 - 2017 - Paper 1
Step 1
Step 2
Calculate Favorable Outcomes
Answer
Next, we find the number of favorable outcomes where all three crosses are in the same row, column, or diagonal.
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Rows: There are 3 rows, and in each row, we can choose all 3 squares in exactly one way. Therefore:
- Favourable outcomes for rows = 3.
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Columns: Similar to rows, there are also 3 columns:
- Favourable outcomes for columns = 3.
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Diagonals: There are 2 diagonals:
- Favourable outcomes for diagonals = 2.
Adding these gives us:
Step 3