How do I calculate this problem and is there a way to do it on a TI-84plus?

Question

if there is a 35% chance of rain every day for the next four days, what is the probability that it will rain every day for the four days?

Answer 1

One of the most straightforward ways to approach this problem would be to consider it day by day:

What's the probability it rains on the first day (ignoring the other days)? .35

What's the probability it rains on the first day and the second day (ignoring the other days)? This requires us to take the probability that it will rain the first day (.35) and multiply it by the probability it will rain on the second day (.35), giving us: .35×.35 or .35²

What's the probability it rains on the first, second, and third days (ignoring the fourth day)? That requires us to take the probability it will rain the first two days (.35²) and multiply it be the probability it will rain on the third day (.35), giving us: .35²×.35, or .35³.

Hopefully at this point you can identify a pattern. The probability that it will rain on the first, second, third, and fourth days is that probability of it raining on the first three days (.35³) times the probability it will rain on the fourth (.35), giving us: .35⁴.

As far as doing this on your calculator, once you work out the problem and identify the pattern, it's a simple solution of entering .35⁴ into your calculator. This pattern would hold for any number of days, as long as they all had the same probability of rain.