Independent solution

How to solve this Conditional Probability question

Setup

Setup

Let x be the probability of the three-way cell. Solve the supplied conditional ratio to obtain x=0.06.

xx+0.12=13,x=0.06\frac{x}{x+0.12}=\frac13,\qquad x=0.06

Model

Model

The eight membership cells partition the sample space. Subtract the three one-event cells, three two-event cells, and the three-way cell to obtain the none cell.

p0=1−3(0.10)−3(0.12)−0.06=0.28p_0=1-3(0.10)-3(0.12)-0.06=0.28

Compute

Compute

The none cell is 0.28 and the conditioning event A complement has probability 0.60, so the conditional ratio is 0.28/0.60=0.4667.

Pr⁡(Ac)=1−0.10−2(0.12)−0.06=0.60\Pr(A^c)=1-0.10-2(0.12)-0.06=0.60
Pr⁡(none∣Ac)=0.28/0.60\Pr(\text{none}\mid A^c)=0.28/0.60

Answer

Answer

The requested conditional probability rounds to 0.467, corresponding to choice C.

0.467(C)\boxed{0.467\quad\text{(C)}}