SOLUTION: 52% of all statistics classes require a statistical calculator and 30% require the use of a computer that has statistical software. Of the classes that require a statistical calcul

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Question 1192353: 52% of all statistics classes require a statistical calculator and 30% require the use of a computer that has statistical software. Of the classes that require a statistical calculator, 16% also require the use of a computer.

P
(Requires a Statistical Calculator)
=

P
(Requires a Statistical Software)
=
P
(Requires a Statistical Calculator and Statistical Software)
=

P
(Requires a Statistical Calculator GIVEN It Requires Statistical Software)
=

Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website!
Certainly, let's break down the given information and calculate the probabilities.
**Given:**
* P(Requires Statistical Calculator) = 0.52
* P(Requires Statistical Software) = 0.30
* P(Requires Statistical Calculator and Statistical Software | Requires Statistical Software) = 0.16
**To find:**
* P(Requires Statistical Calculator and Statistical Software)
* P(Requires Statistical Calculator | Requires Statistical Software)
**Calculations:**
* **P(Requires Statistical Calculator and Statistical Software)**
* We know: P(A | B) = P(A ∩ B) / P(B)
* Where:
* A: Requires Statistical Calculator
* B: Requires Statistical Software
* Therefore:
* P(A ∩ B) = P(A | B) * P(B)
* P(Requires Statistical Calculator and Statistical Software) = 0.16 * 0.30 = **0.048**
* **P(Requires Statistical Calculator | Requires Statistical Software)**
* This is already given in the problem statement: **0.16**
**In summary:**
* P(Requires Statistical Calculator) = 0.52
* P(Requires Statistical Software) = 0.30
* P(Requires Statistical Calculator and Statistical Software) = 0.048
* P(Requires Statistical Calculator | Requires Statistical Software) = 0.16

Answer by ikleyn(52835)   (Show Source):
You can put this solution on YOUR website!
.
52% of all statistics classes require a statistical calculator and
30% require the use of a computer that has statistical software.
Of the classes that require a statistical calculator, 16% also require the use of a computer.

(a) P(Requires a Statistical Calculator) =

(b) P(Requires a Statistical Software) =

(c) P(Requires a Statistical Calculator and Statistical Software) =

(d) P(Requires a Statistical Calculator GIVEN It Requires Statistical Software) =
~~~~~~~~~~~~~~~~~~~~~~~~~~~

        In the post by @PChill, the solution and the answers for (c) and (d) are INCORRECT.
        I came to bring correct solutions.

(a) P(Requires a Statistical Calculator) = 0.52 (given). (b) P(Requires a Statistical Software) = 0.30 (given). (c) P(Requires a Statistical Calculator and Statistical Software) = 0.52*0.16 = 0.0832. (d) P(Requires a Statistical Calculator GIVEN It Requires Statistical Software) = = 0.277333333.

Solved (correctly).