S1 Probability
Sample space diagrams
and tree diagrams
Sample Space Diagrams
Two fair spinners are numbered 1,1,1,2,3 and 1,2,2,3,3.
The sum of the two numbers is calculated.
a) Find the probability that the sum is exactly 6
b) Find the probability that the sum is less than 6
+
1
1
1
2
3
1
2
2
2
3
4
2
3
3
3
4
5
2
3
3
3
4
5
3
4
4
4
5
6
3
4
4
4
5
6
P(6) = 2
25
P(<6) = 23
25
Tree Diagrams
Adam and Beth are playing darts. The probability that Adam
hits the board with his first dart is 0.4 and the probability
that Beth hits the board with her first dart is 0.6.
Find the probability that:
a) Both Adam and Beth hit with their first dart
b) At least one of them hits with their first dart
B hit P(hit,hit) = 0.4x0.6 = 0.24
0.6
A hit
0.4
0.4
0.6
B missP(hit,miss)=0.4x0.4= 0.16
B hit P(miss,hit)=0.6x0.6= 0.36
0.6
A miss
0.4
B miss
P(at least one hit)
=0.24+0.16+0.36 = 0.76
Questions
1. Throwing a die and tossing a coin. Find the probability of
a head and a 6
2. Throwing two six sided dice and recording the product of
the values. Find the probability that the answer is greater
than or equal to 24
3. Picking one card from each of two different standard
packs of cards. What is the probability that the first card
is a heart and the second is not a heart?
4. Picking a bead from a pot containing 2 black, 3 white and
1 red beads. Not replacing it and picking a second bead.
What is the probability that at least one of the beads is
white?