Question

There is a 60% chance of rain on Saturday and a 20% chance of rain on Sunday. Assume that the event that it rains on Saturday is independent of the event that it rains on Sunday. What is the probability that it rains on exactly one day over the weekend

Answer 1

Answer:

$0.56$

Step-by-step explanation:

GIVEN: There is a $60\%$ chance of rain on Saturday and a $20\%$ chance of rain on Sunday. Assume that the event that it rains on Saturday is independent of the event that it rains on Sunday.

TO FIND: What is the probability that it rains on exactly one day over the weekend.

SOLUTION:

Probability of rain on Saturday $P(A)=0.6$

Probability of not raining on Saturday $P(A^{'}) =1-0.6=0.4$

Probability of rain on Sunday $P(B)=0.2$

Probability of not raining on Saturday $P(B^{'})=1-0.2=0.8$

Probability of raining exactly one day over the weekend

 $=\text{Probability it rains only on Saturday}+\text{Probability it rains only on Sunday}$

$=P(A)\times P(B^{'})+P(B)\times P(A^{'})$

$=0.6\times0.8+0.2\times0.4$

$=0.56$

Hence probability of raining exactly only one day over the weekend is $0.56$