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 mark] What is the probability that two attend one locationand two attend another same location?
- [1 mark] What is the probability that no tourists hop off atthe Distillery District and Bata Shoe Museum?
- [1 mark] What is the probability that at least one tourist getsoff at Casa Loma?
Answer:
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
= 0.0820 Answer 1
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
= 0.3164 Answer2
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
= 0.4138 Answer 3
DONE