Question

Use the following probabilities to answer the question. It may be helpful to sketch a Venn diagram.

P(A)=0.5 ,P(B)=0.3 and P(A and B)=0.20.
P(B∣ not A)=

Answer 1

Answer: To find P(B|not A), we need to first find P(not A). We know that:

P(A) = 0.5

Therefore,

P(not A) = 1 - P(A) = 1 - 0.5 = 0.5

Next, we need to find P(B and not A). We know that:

P(A and B) = 0.20

We can rearrange this to solve for P(B and A):

P(B and A) = P(A and B) = 0.20

Since P(B and not A) and P(B and A) are mutually exclusive (meaning they cannot happen at the same time), we can use the following formula:

P(B and not A) = P(B) - P(B and A)

Substituting in our values, we get:

P(B and not A) = P(B) - P(B and A) = 0.3 - 0.20 = 0.1

Now we can find P(B|not A) using the formula:

P(B|not A) = P(B and not A) / P(not A)

Substituting in our values, we get:

P(B|not A) = P(B and not A) / P(not A) = 0.1 / 0.5 = 0.2

Therefore, P(B|not A) is 0.2 or 20%.

Explanation: