Probability

Question code: 15021

Question 2202

To predict the weather for three days (Monday, Tuesday and Wednesday), a simple computer simulation uses the following model to determine the likelihood of rain.

The probability that it rains on Monday is

{\frac{1}{5}.}

For Tuesday and Wednesday, the probability of rain is

twice the probability of rain the previous day if it rained the previous day,
the same as the probability of rain the previous day if it did not rain the previous day.

(i)

Construct a probability tree showing this information

(ii)

Find the probability that it rains on all three days.

(iii)

Find the probability that it rains on at most two days.

(iv)

Find the probability that it rains on Wednesday, given that it rained on exactly one day.

Answer

(ii)

{\frac{8}{125}.}

(iii)

{\frac{117}{125}.}

(iv)

{\frac{16}{37}.}

Question code: 15021