Back to Explorer Missions
Alex created a computer program called “The Number Transformer”. The program works as follows:
1. It starts with a set of six numbers: {2, 3, 4, 5, 6, 7}.
2. The program randomly selects one of these numbers.
3. If the selected number is even, all even numbers in the set are decreased by 1.
4. If the selected number is odd, all odd numbers in the set are increased by 2.
5. After this transformation, the program selects another number from the new set.
Alex runs the program once, and it performs steps 1-4. Then Alex runs it a second time, but due to a glitch, the set doesn’t change after the second selection.
What is the probability that the number 5 was selected on the second run?
Let’s solve this step-by-step:
1. Initial set: {2, 3, 4, 5, 6, 7}
2. First run possibilities:
a) If an even number is selected (2, 4, or 6):
– Probability: 3/6 = 1/2
– New set: {1, 3, 3, 5, 5, 7}
b) If an odd number is selected (3, 5, or 7):
– Probability: 3/6 = 1/2
– New set: {2, 5, 4, 7, 6, 9}
3. Second run probabilities:
a) If the first run selected an even number:
– Probability of selecting 5: 2/6 = 1/3
b) If the first run selected an odd number:
– Probability of selecting 5: 1/6
4. Total probability calculation:
P(selecting 5 on second run) = P(even first) × P(5 after even) + P(odd first) × P(5 after odd)
= (1/2 × 1/3) + (1/2 × 1/6)
= 1/6 + 1/12
= 3/12
= 1/4
Therefore, the probability that the number 5 was selected on the second run is 1/4 or 25%.
Remember, at QMAK, we don’t just teach; we empower. We don’t just inform; we inspire. We don’t just question; we act. Become a Gold Member, and let’s unlock your child’s full potential, one question at a time.