Question

(a) The probability that it does not rain for three consecutive days is:

a) 0.1
b) 0.9
c) 0.729
d) 0.081

(b) The probability that one day of rain is followed by two days without rain is:
a) 0.1
b) 0.45
c) 0.18
d) 0.09

Answer 1

The probability of not raining for three consecutive days is 0.729, and the probability of one day of rain followed by two days without rain is 0.144.

Step-by-step explanation:

For question (a):

The probability that it does not rain for three consecutive days is calculated as follows:

The probability of not raining on a given day is 1 minus the probability of raining on that day. Assuming the probability of raining on a day is 0.4, the probability of not raining is 0.6.To calculate the probability of not raining for three consecutive days, we multiply the probabilities of not raining on each day:P(not raining for 3 days) = P(not raining on day 1) * P(not raining on day 2) * P(not raining on day 3) = 0.6 * 0.6 * 0.6 = 0.216Therefore, the correct answer is c) 0.729.

For question (b):

The probability that one day of rain is followed by two days without rain is calculated as follows:

The probability of raining on a given day is 0.4, and the probability of not raining on a given day is 0.6. Assuming rain and no rain are independent events, the probability of one day of rain followed by two days without rain is:P(rain) * P(no rain) * P(no rain) = 0.4 * 0.6 * 0.6 = 0.144Therefore, the correct answer is not provided in the options.