Probability Tree diagrams

1
Probability Tree diagrams
Example A coin is tossed twice. Complete the
probability tree diagram showing all the possible
outcomes and the probability of each. What is
the probability of the two tosses giving the same
result?
1st throw
2nd throw
Head
Head, Head
Head
Tail
Head, Tail
Head
Tail, Head
Tail
Tail
Tail, Tail
2
Example A six sided dice is thrown twice.
Complete the tree diagram showing all the
probabilities
1st throw
2nd throw
four
four, four
four
Not four
four, Not four
Four
Not four, four
Not 4
Not four
Not four, Not four

• What is the probability of throwing a total of
• two fours?
• No fours?
• At least one four?

3
Example It is found that the probability of a
particular brand of firework will not light is
?. John buys two. Copy and complete the tree
diagram and use it to find the probability that
both of his fireworks light.
4
Example When cultivating fruit bushes by planting
cuttings the probability that a cutting produces
a bush is 3/5. Find the probabilities of 0, 1, 2
bushes being produced, if two cuttings are
planted.
1st cutting
2nd cutting
Bush
Bush, Bush
Bush
No Bush
Bush, No Bush
Bush
No Bush, Bush
No Bush
No Bush
No Bush, No Bush
5

• Example
• A box contains seven red and three blue pens.
  Jane takes a pen from the box and keeps it then
  Susan takes a pen from the box. Both girls make
  their selection without looking at the colour.
• Draw a tree diagram to show the possible colours
  each has selected.
• Use your tree diagram to find the probability
  that Jane and
• Susan
• (i) each select a red pen
• (ii) select pens of the same colour.