Question

The local weather person has been accurate in her predictions within 2 degrees temperature forecast 80% of the time. Find the probability that she is accurate...

a) exactly 3 out of the next 5 days
b) at least 4 of the next 5 days

Answer 1

A) 0.2048
B) 0.7373

To find the probability that she is correct exactly 3 days, we have

`_5C_3(0.8)^3(1-0.8)^(5-3) \\ \\(5!)/(3!2!)(0.8)^3(0.2)^2=0.2048`

To find the probability that she is right at least 4 of the 5 days, we find the probability she is right 4 days, the probability she is right 5 days, and add them together:

`_5C_4(0.8)^4(1-0.8)^(5-4)+_5C_5(0.8)^5(1-0.8)^(5-5) \\ \\(5!)/(4!1!)(0.8)^4(0.2)^1+(5!)/(5!0!)(0.8)^5(0.2)^0 \\ \\5(0.8)^4(0.2)+0.8^5=0.4096+0.32768=0.73728\approx0.7373`