Download Understanding Data Handling and Probability

Understanding Data Handling and Probability
4.1 Use the language and notation of probability.
4.2 Find probabilities using theoretical models (with equally likely events) or relative
frequencies.
4.3 Calculate the probability of a single or two successive events including the sum of
the probabilities of mutually exclusive events
Questions
1.
Ashby Ladies’ hockey team plays a league match on Saturday against the
team at the top of the league.
(4.1, 4.2)
(a) What are the possible outcomes of the game?
(b) Are these outcomes equally likely?
2.
Which of these situations are independent? Explain your answers
(a) Tossing a coin twice
(b) Picking (and eating) two Smarties from a bag of 10 Smarties of mixed
colours. Are the colours picked independent?
(c) Passing an exam in Maths and an exam in Science
(d) Rolling two dice and getting a six on both.
3.
On your way to college you encounter two sets of traffic lights. The probability
that the first set is green is 0.4. If the first is green then the probability that the
second set is green is 0.8, while if the first is red then the probability that the
second is green is 0.6.
(4.3)
Draw a tree diagram
Calculate the probability that you have to stop at:
(a) both sets of lights
(b) neither set of lights
4.
A spinner has a probability of ½ of landing on red and equal probabilities of ¼
of landing on green or yellow. The spinner is spun twice.
(4.2, 4.3)
(a) Draw a tree diagram to illustrate all the possible outcomes of the two
spins.
(b) Calculate the probability of getting 2 yellows
(c) Calculate the probability of getting the same colour both times.
(d) What is the probability of getting a different colour on the two spins?
(e) What is the probability of getting green on neither of the two spins?
Answers:
1 (a)
(b)
win, lose, draw
no
2 (a) independent, one result does not affect the next
(b) no, because if you eat a red Smartie there will be one fewer red to pick next time
(c) Possibly: do you believe that people who are good at maths are also good at
science
(d) independent
3.
first set
second set
0.8
0.4
Green
GG
0.32
0.2
Red
GR
0.08
0.6
Green
RG
0.36
Red
RR
0.24
Green
Red
0.6
0.4
(a)
(b)
P(stop at both sets) = 0.24
P(stop at neither set) = 0.32
4.
First spin
Red
½
second spin
½
Red
RR
¼
¼
green
RG
1/8
¼
Yellow
RY
1/8
½
Red
GR
1/8
¼
green
GG
1/16
¼
Yellow
GY
1/16
½
Red
YR
1/8
¼
green
YG
1/16
Yellow
YY
1/16
¼
Green
¼
Yellow
¼
a) tree
b) P(y,y) = 1/16
c) P(same colour)=
P(RR or GG or YY) =
¼ + 1/16 + 1/16 = 6/16
or 3/8
d) P(different colour) =
1 – 3/8 = 5/8
e) P(G on neither) =
¼ + 1/8 + 1/8 + 1/16 =
9/16