Pat throws a fair coin n times - Edexcel - GCSE Maths - Question 21 - 2021 - Paper 3
Question 21
Pat throws a fair coin n times.
Find an expression, in terms of n, for the probability that Pat gets at least 1 head and at least 1 tail.
Worked Solution & Example Answer:Pat throws a fair coin n times - Edexcel - GCSE Maths - Question 21 - 2021 - Paper 3
Step 1
Find the total number of outcomes
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Answer
When Pat throws a coin n times, the total number of possible outcomes is given by:
2n
This includes all possible combinations of heads and tails.
Step 2
Calculate the probability of all heads or all tails
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Answer
The only outcomes that do not satisfy the condition of getting at least one head and at least one tail are:
All heads: 1 outcome (HHH...H)
All tails: 1 outcome (TTT...T)
Thus, the total number of outcomes that do not meet the requirement is:
2.
Step 3
Determine the required probability
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Answer
To find the probability that Pat gets at least 1 head and at least 1 tail, we subtract the undesired outcomes from the total outcomes and divide by the total outcomes:
