# probability of 0.3 for a sunny day any day in jan,need to work out 2 other probabilities for 2 days

The probability that it is sunny on any day in January is $0.3$. Find the probability that for two days in January

a) it will be sunny on both days.

b) it will be sunny on one of these days.

• Any thoughts? Note: the problem can not be answered without information regarding dependence. Presumably you are meant to assume independence, though that should be stated (and it isn't clear that it is a realistic assumption). – lulu Jun 6 '18 at 13:11

$P(A \cap B) = P(A) * P(B)$ $\therefore P(\text{2 given days will both be sunny}) = 0.3 * 0.3 = 0.09$
b) for mutually exclusive events: $P(A \cup B) = P(A) + P(B)$ $\therefore P(\text{2 given days, at least one is sunny}) = 0.3 + 0.3 = 0.6$