Question

You are meeting your friend for dinner at 7pm. You have a 1/3 chance of arriving after 7pm. Your friend has a 40% chance of arriving by 7pm. What is the approximate chance that both of you are eating at 7pm together?

Answer 1

To calculate the chance that both you and your friend are eating at 7pm together, multiply your chance of arriving by 7pm (2/3) by your friend's chance (0.4), resulting in approximately a 26.7% chance.

Step-by-step explanation:

The question asks to calculate the approximate chance that both you and your friend are eating at 7pm together. The question provides the information that you have a 1/3 chance of arriving after 7pm, which implies a 2/3 chance of arriving by 7pm. Since your friend has a 40% chance (or 0.4 probability) of arriving by 7pm, we need to multiply your probability of arriving by 7pm by your friend's probability to find the joint probability of both events occurring.

To calculate this, we follow these steps:

1. Calculate your chance of arriving by 7pm: 1 - 1/3 = 2/3.
2. Calculate your friend's chance of arriving by 7pm which is already given as 0.4.
3. Multiply these probabilities together to find the joint probability: (2/3) * (0.4) = 8/30 or approximately 0.267 or 26.7%.

So, there is approximately a 26.7% chance that both you and your friend will be eating at 7pm together.