2.3 Conditional Probabilities in Venn Diagrams

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Question 14

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 Conditional Probabilities in Venn Diagrams

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Question 14

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 Conditional Probabilities in Venn Diagrams

Question 14

Markscheme

2.3 Conditional Probabilities in Venn Diagrams

Question 14

Markscheme

2.3 Conditional Probabilities in Venn Diagrams

Question 14

2.3 Conditional Probabilities in Venn Diagrams Questions

2.3 Conditional Probabilities in Venn Diagrams

Question 14

2.3 Conditional Probabilities in Venn Diagrams Questions