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A pharmaceutical company run a clinical trial for a new flu vaccine. 1200 people volunteered to take part. 625 of the volunteers were given the real flu vaccine. The remaining 575 volunteers received a harmless placebo drug (which in principle would have no positive or negative effect).

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 The pharmaceutical company believe that the flu vaccine could cause dizziness in some adults.

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 165 of the volunteers who had the real flu vaccine reported dizziness.

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81 of the volunteers who had the placebo drug reported dizziness.

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Determine the probability that a volunteer will not suffer dizziness. Give your answer to 3 decimal places.

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Given that a person has dizziness, what is the probability that they have had the real flu vaccine? Give your answer to 3 decimal places.

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The pharmaceutical company find that 1% of people who have the vaccine suffer a more serious side effect (fainting). The company take a random sample of 40 people.

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 What is the probability that exactly 2 people have the serious side effect in this sample of 40? Give your answer to 3 decimal places.

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What is the probability that at least 2 people have the serious side effect in this sample of 40? Give your answer to 3 decimal places.

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