Question

A friend asks you to guess if it will rain two days in a row. If you are correct on both days, your friend will pay for dinner, if you are incorrect on either day, you will have to pay for dinner. You tell your friend you think it will rain on both days. Later, you see the weather forecast for each day. There is a 70% chance of rain on the first day and a 60% chance of rain on the second day. Who would you expect to pay for dinner?

Answer 1

A friend asks me to guess if it will rain two days in a row.

If I am correct on both days, my friend will pay for dinner.

If I am incorrect on either day, I would have to pay for dinner.

Now, I predict that it will rain on both days.

There is a 70% chance of rain on the first day, and a 60% chance of rain on the second day.

So, the probability of raining on the first day is 0.7, and the chance of raining on the second day is 0.6.

Now, as raining on two different days are independent of each other, so

the chance that it will rain on both days is

=0.7*0.6

=0.42

So, the chance that I am correct on both days is 0.42.

So, i am incorrect on either, or both of the days, with chance (1-0.42), ie. 0.58.

So, I would expect that it would be me who would have to pay for dinner.