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VCE Methods Probability Application Task 6
Adapted for Year 11. Unit 1 & 2.
Number of marks: 4
Reading time: 1 minute
Writing time: 6 minutes
Section B – Calculator Allowed
Instructions
• Answer all questions in the spaces provided.
• Write your responses in English.
• In questions where a numerical answer is required, an exact value must be given unless otherwise specified.
• In questions where more than one mark is available, appropriate working must be shown.
• Unless otherwise indicated, the diagrams in this book are not drawn to scale.
Mika is flipping a coin. The unbiased coin has a probability of \( \frac{1}{2} \) of landing on heads and \( \frac{1}{2} \) of landing on tails.
Let \( X \) be the binomial random variable representing the number of times that the coin lands on heads. Mika flips the coin five times.
a. i. Find \( \Pr(X = 5) \). 1 mark
ii. Find \( \Pr(X \geq 2) \). 1 mark
iii. Find \( \Pr(X \geq 2 \mid X < 5) \), correct to three decimal places. 2 marks
End of examination questions
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