Question

The probability that is rains on Monday is 0.4. The probability that it rains on Tuesday is 0.8. The probability tree diagram shows this informaiton.

image

What is the probability that there will be no rain on Monday and no rain on Tuesday?

A.
0.2

B.
0.8

C.
0.12

D.
0.48

Answer 1

To find the probability that there will be no rain on Monday and no rain on Tuesday, we can use the given probabilities:

- The probability that it rains on Monday, \( P(\text{Rain on Monday}) = 0.4 \).
- Therefore, the probability that it does not rain on Monday, \( P(\text{No rain on Monday}) = 1 - P(\text{Rain on Monday}) = 1 - 0.4 = 0.6 \).

- The probability that it rains on Tuesday, \( P(\text{Rain on Tuesday}) = 0.8 \).
- Therefore, the probability that it does not rain on Tuesday, \( P(\text{No rain on Tuesday}) = 1 - P(\text{Rain on Tuesday}) = 1 - 0.8 = 0.2 \).

Now, to find the probability of both events happening (no rain on Monday and no rain on Tuesday), we multiply the probabilities:

\[
P(\text{No rain on Monday and No rain on Tuesday}) = P(\text{No rain on Monday}) \times P(\text{No rain on Tuesday}) = 0.6 \times 0.2 = 0.12
\]

Thus, the probability that there will be no rain on Monday and no rain on Tuesday is \( 0.12 \).

The correct answer is \( C. \, 0.12 \).