2.3.3 Conditional probability (A-level only)

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Question 95

A marine biologist analyzes 200 water samples from a local estuary for the presence of three specific pollutants: Nitrates ( $N$ ), Phosphates ( $P$ ), and Microplastics ( $M$ ). The frequencies of these pollutants found in the samples are summarized as follows:

110 samples contained none of the pollutants.
18 samples contained only Nitrates.
22 samples contained only Phosphates.
14 samples contained only Microplastics.
10 samples contained Nitrates and Phosphates, but not Microplastics.
12 samples contained Nitrates and Microplastics, but not Phosphates.
8 samples contained Phosphates and Microplastics, but not Nitrates.
6 samples contained all three pollutants.

A sample is selected at random from the 200.

Find the probability that the sample does not contain Microplastics.

[2]

Find $\cap P \cap M')$ .

[2]

Find $\cup P \cup M')$ .

[2]

Find the probability that the sample contains at most one type of pollutant.

[2]

Given the selected sample has at most one type of pollutant, find the probability it contains Nitrates.

[3]

The random variable $X\,$ is the number of the pollutants $N$ , $P$ , $M\,$ found in a randomly selected sample.

Find $E (X)$ .

[3]

2.3.3 Conditional probability (A-level only)

Question 95

110 samples contained none of the pollutants.
18 samples contained only Nitrates.
22 samples contained only Phosphates.
14 samples contained only Microplastics.
10 samples contained Nitrates and Phosphates, but not Microplastics.
12 samples contained Nitrates and Microplastics, but not Phosphates.
8 samples contained Phosphates and Microplastics, but not Nitrates.
6 samples contained all three pollutants.

A sample is selected at random from the 200.

Find the probability that the sample does not contain Microplastics.

[2]

Find $\cap P \cap M')$ .

[2]

Find $\cup P \cup M')$ .

[2]

Find the probability that the sample contains at most one type of pollutant.

[2]

Given the selected sample has at most one type of pollutant, find the probability it contains Nitrates.

[3]

The random variable $X\,$ is the number of the pollutants $N$ , $P$ , $M\,$ found in a randomly selected sample.

Find $E (X)$ .

[3]

2.3.3 Conditional probability (A-level only)

Question 95

2.3.3 Conditional probability (A-level only) Questions

2.3.3 Conditional probability (A-level only)

Question 95

2.3.3 Conditional probability (A-level only) Questions