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?

3 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.

3 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!

3 years ago

## Answered By Sara S

Note:

A\cap B is A intersect B

A\cup B is A union B