Tree Diagrams

A computer uses the numbers 1, 2, or 3 at random to make three-digit numbers. Assuming that a number can be repeated, show on a tree diagram all the possible combinations that the computer can print.

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A computer uses the numbers 1, 2, or 3 at random to make three-digit numbers.

Calculate the probability of getting the number 131.

Answer explanation

Out of the 27 possible outcomes, there is only 1 possibility of getting number 131.

Therefore, the probability of getting number 131 is 1/27.

A computer uses the numbers 1, 2, or 3 at random to make three-digit numbers.

Calculate the probability of getting an even number.

Answer explanation

Out of the 27 possible outcomes, there are 9 even numbers (112, 122, 132, 212, 222, 232, 312, 322, and 332).

Therefore, the probability of getting an even number is 9/27 or 1/3.

A computer uses the numbers 1, 2, or 3 at random to make three-digit numbers.

Calculate the probability of getting a multiple of 11.

Answer explanation

Out of the 27 possible outcomes, there are 3 numbers that are multiple of 11 (121, 132 and 231).

Therefore, the probability of getting a multiple of 11 is 3/27 or 1/9.

A computer uses the numbers 1, 2, or 3 at random to make three-digit numbers.

Calculate the probability of getting a multiple of 3.

Answer explanation

Out of the 27 possible outcomes, there are 9 numbers that are multiple of 3 (111, 123, 132, 213, 222, 231, 312, 321, and 333).

Therefore, the probability of getting a multiple of 3 is 9/27 or 1/3.

A computer uses the numbers 1, 2, or 3 at random to make three-digit numbers.

Calculate the probability of getting a multiple of 2 or 3.

Answer explanation

Out of the 27 possible outcomes, there are 9 numbers that are multiple of 2 (112, 122, 132, 212, 222, 232, 312, 322, and 332).

Also out of the 27 possible outcomes, there are 9 numbers that are multiple of 3 (111, 123, 132, 213, 222, 231, 312, 321, and 333).

Therefore, the probability of getting a multiple of 2 or 3 is 9/27 + 9/27 = 18/27 or 2/3.

A particular board game involves players rolling a dice. However, before a player can start, they need to roll a 6.

Calculate the probability of getting a six on the first throw.

• 1/6
• 1/3
• 1/2
• 2/3

A particular board game involves players rolling a dice. However, before a player can start, they need to roll a 6.

Calculate the probability of starting within the first two throws.

• 1/6
• 1/3
• 1/36

• 5/36

A particular board game involves players rolling a dice. However, before a player can start, they need to roll a 6.

Calculate the probability of starting on the second throw.

• 1/6
• 1/3
• 1/36

• 5/36

A particular board game involves players rolling a dice. However, before a player can start, they need to roll a 6.

Calculate the probability of not starting within the first three throws.

• 91/216

• 125/216

• 1/36

• 5/36