# Question 4 [3 marks] Four tour

Question 4 [3 marks]

Four tourists plan on taking a bus tour around Toronto. Thistour allows them to hop on and off the bus at any of the 8 stopsavailable. The available stops are the CN tower, Harbour Front,Queen’s Quay, Dundas Square, Casa Loma, Distillery District, BataShoe Museum and the Royal Ontario Museum.

1. [1 mark] What is the probability that two attend one locationand two attend another same location?
2. [1 mark] What is the probability that no tourists hop off atthe Distillery District and Bata Shoe Museum?
3. [1 mark] What is the probability that at least one tourist getsoff at Casa Loma?

Solution

Back-upTheory

Probability of an event E, denoted by P(E) = n/N……………………………….……………(1)

where

n = n(E) = Number of outcomes/cases/possibilities favourable tothe event E and

N = n(S) = Total number all possibleoutcomes/cases/possibilities.

Now to work out thesolution,

There are 4 tourists and 8 locations. Since the same locationcan be visited by

more than one tourist, total number of possible location visits= 84 = 4096 …………….. (2)

Hence, vide (1), N = 4096………………………………………………………………………………….(3)

Part (a)

Two attending one location can any 2 out of 4 tourists in4C2 = 6 ways. Then, the two necessarily visitanother location. Thus, there is only one possibility.

Now, the first pair can choose any one of 8 locations in 8 waysand then the second

pair can choose only one of the remaining 7 locations.

So, total number of possibilities = 6 x 8 x 7 = 336 and hencevide (1), n = 336 ………… (4)

Finally, vide (1), (3) and (4),

Probability that two attend one location and two attend anotherlocation = 336/4096

Part (b)

If no tourists hop off at the Distillery District and Bata ShoeMuseum, the number of

location choices reduces from 8 to 6. Hence, total number ofpossible location visits

= 64 = 1296 and this then becomes n vide(1)………………………………………………………..(5)

Thus, vide (1), (3) and (5),

Probability that no tourist hop off at the Distillery Districtand Bata Shoe Museum

= 1296/4096

Part (c)

Probability that at least one tourist gets off at Casa Loma

= 1 –P(no tourist gets off at Casa Loma)

No tourist gets off at Casa Loma => the number of locationchoices reduces from

8 to 7. Hence, total number of possible location visits =74 = 2401 and this then

becomes n vide(1)……………………………………………………………………………………………(6)

Thus, vide (1), (3) and (6),

Probability that at least one tourist gets off at Casa Loma

= 1 – (2401/4096)

= 1 – 0.5862

DONE

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