Jenna estimates that she has an 85% chance of finishing her Math homework and a 70% chance of finishing her science homework. What is the probability that she won't finish either homework?
4 years ago
Answered By Sara S
We first define two events A and B as follows:
A:= finishing Math homework
B:= finishing science homework
If P(A) and P(B) show the probability of events A and B, respectively, we have
P(A) = 85% or 0.85
P(B) = 70% or 0.7
The question wants us to find out P(D) where
D:= not finishing either homework
We have D = \overline{A\cup B} which means D is the complement of the event A union B.
So we have
P(D) = 1- P(A\cup B)
and we have
P(A\cup B) = P(A) + P(B) - P(A\cap B).
In the formula above, we do not know what is P(A\cap B).
We assume A and B are independent and so
P(A\cap B) = P(A)xP(B) = 0.85x0.7 = 0.595.
Hence
P(A\cup B) = P(A) + P(B) - P(A\cap B) = 0.955.
Finally, we find
P(D)= 1- P(A\cup B) = 1- 0.955 =0.045 or 4.5%.
You may use different notations based on your notes from the lecture.
4 years ago
Answered By Sara S
We first define two events A and B as follows:
A:= finishing Math homework
B:= finishing science homework
If P(A) and P(B) show the probability of events A and B, respectively, we have
P(A) = 85% or 0.85
P(B) = 70% or 0.7
The question wants us to find out P(D) where
D:= not finishing either homework
We have D = \overline{A\cup B} which means D is the complement of the event A union B.
So we have
P(D) = 1- P(A\cup B)
and we have
P(A\cup B) = P(A) + P(B) - P(A\cap B).
In the formula above, we do not know what is P(A\cap B).
We assume A and B are independent and so
P(A\cap B) = P(A)xP(B) = 0.85x0.7 = 0.595.
Hence
P(A\cup B) = P(A) + P(B) - P(A\cap B) = 0.955.
Finally, we find
P(D)= 1- P(A\cup B) = 1- 0.955 =0.045 or 4.5%.
You may use different notations based on your notes from the lecture.
Best!
4 years ago
Answered By Sara S
Note:
A\cap B is A intersect B
A\cup B is A union B