Questions: Refer to the Venn diagram to the right for events A and B in an equally likely sample space S. Find S the indicated probability. P((A ∩ B)′) P((~A ∩ ~B)′)= (Type a decimal.)

Refer to the Venn diagram to the right for events A and B in an equally likely sample space S. Find S the indicated probability.
P((A ∩ B)′)
P((~A ∩ ~B)′)=
(Type a decimal.)
Transcript text: Refer to the Venn diagram to the right for events A and B in an equally likely sample space S . Find $S$ the indicated probability. \[ P\left((A \cap B)^{\prime}\right) \] \[ \mathrm{P}\left((\mathrm{~A} \cap \mathrm{~B})^{\prime}\right)= \] $\square$ (Type a decimal.)
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Solution

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Solution Steps

Step 1: Calculate the number of elements in A∩B

The intersection of A and B contains 10 elements.

Step 2: Calculate the total number of elements in the sample space S

The total number of elements is the sum of all the numbers in the Venn diagram: 35 + 10 + 30 + 25 = 100.

Step 3: Calculate the number of elements in (A∩B)'

The complement of (A∩B), denoted as (A∩B)', contains all elements in S that are not in (A∩B). Since A∩B has 10 elements and S has 100, (A∩B)' has 100 - 10 = 90 elements.

Step 4: Calculate the probability P((A∩B)')

P((A∩B)') = (Number of elements in (A∩B)') / (Total number of elements in S) P((A∩B)') = 90 / 100 P((A∩B)') = 0.9

Final Answer: The final answer is $\boxed{0.9}$

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