2.3.2 Conditional probability (A-level only)

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Question 97

A botanical research station analyzes 50 plant samples for the presence of three specific enzymes: Alpha ( $A$ ), Beta ( $B$ ), and Gamma ( $Γ$ ). The distribution of these enzymes across the samples is summarized in the following data:

9 samples contain only enzyme $A$ .
6 samples contain both enzymes $A\,$ and $B$ , but not $Γ$ .
11 samples contain only enzyme $B$ .
4 samples contain both enzymes $B\,$ and $Γ$ , but not $A$ .
8 samples contain only enzyme $Γ$ .
12 samples contain none of these enzymes.
No samples contain both $A\,$ and $Γ\,$ simultaneously.

One sample is selected at random.

Show that the probability that the sample contains more than one enzyme is 0.2.

[2]

Determine the probability that the sample contains enzyme $A\,$ or enzyme $B$ (or both).

[2]

State the probability that the sample contains both enzyme $A\,$ and enzyme $Γ$ .

[1]

Given that the sample is found to contain at least one of the three enzymes,

calculate the probability that it contains enzyme $Γ$ .

[3]

Determine, with a reason, whether the presence of enzyme $B\,$ and the presence of enzyme $Γ\,$ in a sample are statistically independent events.

[4]

2.3.2 Conditional probability (A-level only)

Question 97

9 samples contain only enzyme $A$ .
6 samples contain both enzymes $A\,$ and $B$ , but not $Γ$ .
11 samples contain only enzyme $B$ .
4 samples contain both enzymes $B\,$ and $Γ$ , but not $A$ .
8 samples contain only enzyme $Γ$ .
12 samples contain none of these enzymes.
No samples contain both $A\,$ and $Γ\,$ simultaneously.

One sample is selected at random.

Show that the probability that the sample contains more than one enzyme is 0.2.

[2]

Determine the probability that the sample contains enzyme $A\,$ or enzyme $B$ (or both).

[2]

State the probability that the sample contains both enzyme $A\,$ and enzyme $Γ$ .

[1]

Given that the sample is found to contain at least one of the three enzymes,

calculate the probability that it contains enzyme $Γ$ .

[3]

Determine, with a reason, whether the presence of enzyme $B\,$ and the presence of enzyme $Γ\,$ in a sample are statistically independent events.

[4]

2.3.2 Conditional probability (A-level only)

Question 97

Markscheme

2.3.2 Conditional probability (A-level only)

Question 97

Markscheme

2.3.2 Conditional probability (A-level only)

Question 97

2.3.2 Conditional probability (A-level only) Questions

2.3.2 Conditional probability (A-level only)

Question 97

2.3.2 Conditional probability (A-level only) Questions