Ger flips a coin 3 times - Junior Cycle Mathematics - Question 9 - 2019
Question 9
Ger flips a coin 3 times. Each time, he can get heads (H) or tails (T). The diagram in the table below shows how he can get each of the 8 different outcomes.
(a) Co... show full transcript
Worked Solution & Example Answer:Ger flips a coin 3 times - Junior Cycle Mathematics - Question 9 - 2019
Step 1
Write in each of the missing letters (H or T) in the diagram
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Answer
The completed diagram should include the following:
First Flip: H
Second Flip: H, T
Third Flip: H, H, T, T
Resulting in:
H
/ \
H T
/ \ / \
H T H T
The full structure shows HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.
Step 2
Write in the five missing outcomes
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Answer
The five missing outcomes in the table are:
HHT
HTH
HTT
THH
THT
TTH
TTT
Step 3
Write in the number of heads (H) in each of the outcomes
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Answer
Outcome
Number of Heads (H)
HHH
3
HHT
2
HTH
2
HTT
1
THH
2
THT
1
TTH
1
TTT
0
Step 4
Write down the number of outcomes that have no heads
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Answer
Fidelma flips a coin 8 times. The number of outcomes that have no heads is:
Only one outcome: TTTTTTTT.
Step 5
Work out the number of outcomes that have exactly 1 head
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The number of outcomes with exactly 1 head:
The formula to calculate this is given by combinations:
C(8,1)=8
So there are 8 outcomes with exactly 1 head.
Step 6
Work out the total number of outcomes when Fidelma flips the coin 8 times
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The total number of outcomes when Fidelma flips the coin 8 times can be calculated using:
Each flip has 2 outcomes (H or T).
Therefore, the total number of outcomes is:
28=256
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