91Ó°ÊÓ

As per the information given in the question, one notes down the events and assigns them initials. Let’s assign-

L = Legs only

W = Wheels only

LW = Both legs and wheels

N = Neither legs nor wheels

The sample points are – $\left\{\mathbf{L}\mathbf{,}\mathbf{W}\mathbf{,}\mathbf{LW}\mathbf{,}\mathbf{N}\right\}$

Probability is defined as the total number of favorable outcomes from the total number of given outcomes.

Total number of robots designed with legs only = 63

Total number of robots = 106

$$\begin{gathered} \mathbf{Probability}\mathbf{}\mathbf{of}\mathbf{}\mathbf{selecting}\mathbf{}\mathbf{a}\mathbf{}\mathbf{root}\mathbf{}\mathbf{designed}\mathbf{}\mathbf{with}\mathbf{}\mathbf{legs}\mathbf{}\mathbf{only} \\ \mathbf{=}\frac{\mathbf{Total}\mathbf{}\mathbf{number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{robots}\mathbf{}\mathbf{designed}\mathbf{}\mathbf{with}\mathbf{}\mathbf{legs}\mathbf{}\mathbf{only}}{\mathbf{Total}\mathbf{}\mathbf{number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{robots}} \end{gathered}$$

That is, the probability of selecting a robot designed with legs only $$\begin{gathered} \mathbf{=}\frac{\mathbf{63}}{\mathbf{106}} \\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{5943} \end{gathered}$$

Total number of robots with wheels only = 20

Total number of robots = 106

localid="1662213507997" $$\begin{gathered} \mathbf{Probability}\mathbf{}\mathbf{of}\mathbf{}\mathbf{selecting}\mathbf{}\mathbf{a}\mathbf{}\mathbf{robot}\mathbf{}\mathbf{designed}\mathbf{}\mathbf{with}\mathbf{}\mathbf{wheels}\mathbf{}\mathbf{only} \\ \mathbf{=}\frac{\mathbf{Total}\mathbf{}\mathbf{number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{robots}\mathbf{}\mathbf{designed}\mathbf{}\mathbf{with}\mathbf{}\mathbf{wheels}\mathbf{}\mathbf{only}}{\mathbf{Total}\mathbf{}\mathbf{number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{robots}} \end{gathered}$$

Probability of selecting a robot designed with wheels only $\mathbf{=}\frac{\mathbf{20}}{\mathbf{106}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{1886}$

Total number of robots designed with legs and wheels only = 8

Total number of robots = 106

localid="1662213573058" $$\begin{gathered} \mathbf{Probability}\mathbf{}\mathbf{of}\mathbf{}\mathbf{selecting}\mathbf{}\mathbf{a}\mathbf{}\mathbf{robot}\mathbf{}\mathbf{designed}\mathbf{}\mathbf{with}\mathbf{}\mathbf{legs}\mathbf{}\mathbf{and}\mathbf{}\mathbf{wheels} \\ \mathbf{=}\frac{\mathbf{Total}\mathbf{}\mathbf{number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{robots}\mathbf{}\mathbf{designed}\mathbf{}\mathbf{with}\mathbf{}\mathbf{legs}\mathbf{}\mathbf{and}\mathbf{}\mathbf{wheels}}{\mathbf{Total}\mathbf{}\mathbf{number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{robots}} \end{gathered}$$

Probability of selecting a robot designed with legs and wheels $\mathbf{=}\frac{\mathbf{8}}{\mathbf{106}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{0754}$

Total number of robots designed with neither legs nor wheels = 15

Total number of robots = 106

$$\begin{gathered} \mathbf{Probability}\mathbf{}\mathbf{of}\mathbf{}\mathbf{selecting}\mathbf{}\mathbf{a}\mathbf{}\mathbf{robot}\mathbf{}\mathbf{designed}\mathbf{}\mathbf{with}\mathbf{}\mathbf{neither}\mathbf{}\mathbf{legs}\mathbf{}\mathbf{nor}\mathbf{}\mathbf{wheels} \\ \mathbf{=}\frac{\mathbf{Total}\mathbf{}\mathbf{number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{robots}\mathbf{}\mathbf{designed}\mathbf{}\mathbf{with}\mathbf{}\mathbf{neither}\mathbf{}\mathbf{legs}\mathbf{}\mathbf{nor}\mathbf{}\mathbf{wheels}}{\mathbf{Total}\mathbf{}\mathbf{number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{robots}} \end{gathered}$$

Probability of selecting a robot designed with neither legs nor wheels $\mathbf{=}\frac{\mathbf{15}}{\mathbf{106}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{1415}$

The probabilities calculated in steps 1 to 4 can be assigned as $\mathbf{P}\mathbf{\left(}\mathbf{L}\mathbf{\right)}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{5943}\mathbf{,}\mathbf{P}\mathbf{\left(}\mathbf{W}\mathbf{\right)}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{1886}\mathbf{,}\mathbf{P}\mathbf{\left(}\mathbf{LW}\mathbf{\right)}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{0754}\mathbf{,}\mathbf{P}\mathbf{\left(}\mathbf{N}\mathbf{\right)}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{1415}$ respectively.

As we have already calculated it earlier in part (b), Step 2, one notes the probability of selecting a robot designed with wheels only to move further.

We calculated it earlier in part (b), Step 3, which notes down the probability of selecting a robot with legs and wheels to move further.

The probability that the selected robot is designed with wheels is given by the summation of the probability of selecting a robot designed with wheels only and the probability of selecting a robot designed with legs and wheels, that is,

$\mathbf{P}\mathbf{\left(}\mathbf{W}\mathbf{\right)}\mathbf{+}\mathbf{P}\mathbf{\left(}\mathbf{LW}\mathbf{\right)}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{1886}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{0754}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{2640}$

One calculates it earlier in part (b), Step 1, one notes down the probability of selecting a robot designed with legs only as $\mathbf{P}\mathbf{\left(}\mathbf{L}\mathbf{\right)}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{5943}$ to move further.

One calculated it earlier in part (b), Step 3, one notes down the probability of selecting a robot designed with legs and wheels as $\mathbf{P}\mathbf{\left(}\mathbf{LW}\mathbf{\right)}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{0754}$ to move further.

The probability that the selected robot is designed with legs is given by the summation of the probability of selecting a robot with legs only and the probability of selecting a robot with legs and wheels

$\mathbf{P}\mathbf{\left(}\mathbf{L}\mathbf{\right)}\mathbf{+}\mathbf{P}\mathbf{\left(}\mathbf{LW}\mathbf{\right)}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{5943}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{754}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{6697}$