MYP 4 Unit 5 Probability A
1 Choose the correct response, “two events are independent” if
2 When a box of drawing pins was dropped onto the floor, 49 pins landed on their backs and 32
landed on their sides. Estimate, to 2 decimal places, the probability of a drawing pin landing:
on its back …………………..
on its side ……………………
3. 93 people arriving at the beach are asked their age. The results are shown below.
Age
Frequency
0-9
17
10-19
25
20-29
26
30-39
20
40+
5
Assuming they give honest replies, estimate the probability that a randomly selected person on
the beach will be aged:
30 or more …………………….
between 10 and 30 ……………..
4. From past experience, a surfer has a probability of 0.83 of catching a wave. In one week she
tries to catch 75 waves. How many waves do you expect her to catch?
5. A hat contains 12 tickets with the numbers 1 to 12 printed on them. If two tickets are drawn
from the hat without replacement, find the probability that they are both prime numbers.
…………………………….
6.Each morning when Harold has a shower, there is a 90% chance that the hot water is working.
The probability that Harold has a long shower is 80% if the hot water is working, and 10% if the
hot water is not working.
a Find the probability that, on any given day, Harold will have a long shower.
…………………………….
b During a 365 day year, how many long showers would you expect Harold to have?
…………………………….
7. The probability of a delayed flight on a foggy day is fo. When it is not foggy the probability
of a delayed flight is r. The probability of a foggy day is z.
a. Construct a tree diagram to show this information.
FLIGHT
DEL
b. Hence, find the probability of:
i a foggy day and a delayed flight
i a delayed flight
iii a flight which is not delayed
c Comment on your answers to b ii and iii.
8. A class consists of 25 students. 15 have blue eyes, 9 have fair hair, and 3 have both blue eyes
and fair hair.
a. Represent this information on a Venn diagram.
b. Hence, find the probability that a randomly selected student from the class:
¡ has neither blue eyes nor fair hair
ii has blue eyes, but not fair hair
iii has fair hair, given that he or she has blue eyes
iv does not have fair hair, given that he or she does not have blue eyes.
9. A waterpolo player has probability 7 of scoring a goal each time she shoots. If she has 24
shots
at goal, how many goals would you expect her to score?
10. The letters A, B, C, D,........, N are put in a hat.
a. If one of the letters is chosen at random, determine the probability of drawing a vowel
(A, E, I, O, or U) …………………………….
B. Two letters are drawn with replacement.
Copy and complete the tree diagram, including all probabilities.
Hence, determine the probability of drawing:
i a vowel and a consonant …………………………….
i at least one vowel …………………………….
11 A coin is tossed and a die is rolled simultaneously.
a. Illustrate the sample space on a grid.
b. Find the probability of getting:
i a head and an even number …………………………….
ii a 5 or a 6 …………………………….
iii a head and a non-3 …………………………….
iv a head or an even number …………………………….
c. If the experiment is performed twice, find the probability of getting two heads and two
numbers whose sum is 7 …………………………….
12 Two dice are rolled simultaneously.
a. Illustrate the possible outcomes on a 2-dimensional grid.
b. Determine the probability of getting:
i a double 5 …………………………….
ii a sum greater than 9 …………………………….
iii at least one 4 …………………………….
iv a sum of 5 or 6 …………………………….
If the dice were rolled 900 times, on how many occasions would you expect the sum of
the rolls to be prime? …………………………….