Question

In: Math

Suppose a bridge has 10 toll booths in the east-bound lane: four are only for E-Z...

Suppose a bridge has 10 toll booths in the east-bound lane: four are only for E-Z Pass holders, two are only for exact change, one takes only tokens, and the remainder are manned by toll collectors who accept only cash. During heavy-traffic hours it is difficult to see the signs indicating the type of toll booth. Suppose a driver selects a toll booth randomly.

a. What is the probability that an exact-change toll booth is selected?
b. What is the probability that a manual-collection toll booth or the token toll booth is selected?
c. What is the probability that an E-Z Pass toll booth is not selected?
d. Suppose the driver has only tokens. What is the probability of selecting the appropriate toll booth?

Expert Solution

a.

Probability that an exact-change toll booth is selected = Number of booths accepting exact change / Total number of booths

= 2 / 10

= 0.2

b.

Number of manual-collection toll booths = 10 - (4 + 2 + 1) = 3

Probability that a manual-collection toll booth or the token toll booth is selected = (Number of manual-collection toll booths + Number of token toll booths )/ Total number of booths

= (3 + 1) / 10

= 0.4

c.

Probability that an E-Z Pass toll booth is not selected = 1 - Probability that an E-Z Pass toll booth is selected

= 1 - Number of E-Z Pass toll booths / Total number of booths

= 1 - 4/10

= 0.6

d.

If the driver has only token, he.she needs to select token booth which is only one out of 10.

Assuming the driver has no cash and only tokens.

Probability of selecting the appropriate toll booth = Probability of selecting the token toll booth

= Number of token toll booths / Total number of booths

= 1 / 10

= 0.1

milcah answered 1 day ago

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