2. The state highway patrol has determined that one out of every six calls for help originating from roadside call boxes is a hoax. Five calls for help have come in and five tow trucks have been dispatched. 1) What is the probability that none of the calls was a hoax? 2) What is the probability that only three of the callers really needed assistance? 3) If the highway patrol answers 10,000 calls for help next year and each call costs the patrol about $50 (labor, gas, etc.), approximately how much money will be wasted answering false alarms?

Question

contestada

Respuesta :

Cricetus Cricetus · Answer 1 · 2021-09-24T13:17:06+02:00

The probabilities according to the question will be:

(1) 0.4019

(2) 0.1608

(3) "$83350" will be wasted.

For Part (1) and (2),

Let "X" be the hoax calls out of 5 with the probability of each being hoax,

= [tex]\frac{1}{6}[/tex]

→ [tex]X \sim Bin (5, \frac{1}{6} )[/tex]

(1)

→ [tex]P[None \ of \ the \ calls \ was \ hoax (X =0)] = 5_C_o (p)^0 (1-p)^5[/tex]

[tex]= 1\times 1\times (1-\frac{1}{6} )^5[/tex]

[tex]= 0.4019[/tex]

(2)

→ [tex]P[3 \ callers \ needed \ assistance] = P[2 \ calls \ are \ hoax][/tex]

[tex]= P[X=2][/tex]

[tex]= 5_C_2 p^2 (1-p)^3[/tex]

[tex]= 5_C_2 (\frac{1}{6} )^2 (1-\frac{1}{6} )^3[/tex]

[tex]= 0.1608[/tex]

(3) Let X be the hoax calls next year out of 10,000 calls. So, [tex]X \sim Bin (10000, \frac{1}{6} )[/tex]

→ [tex]Expected \ hoax \ calls = np[/tex]

[tex]= 10000\times \frac{1}{6}[/tex]

[tex]= 1666.67[/tex] or, [tex]1667[/tex]

So,

→ [tex]The \ wasted \ money = 50\times 1667[/tex]

[tex]= 83350[/tex] ($)

Thus the above answer is correct.

Learn more about probability here:

https://brainly.com/question/13009213