An automated planetary rover analyzes 400 specific geological sites on Mars. Each site is tested for the presence of specific signatures using three sensors:

Spectrometer ( $S$ )
Magnetometer ( $M$ )
Thermal Imager ( $T$ )

The detection data for these 400 sites is summarized below:

Sensor Detection	$S$	$M$	$T$	$S\,$ and $M$	$S\,$ and $T$	$M\,$ and $T$	All three
Number of Sites	220	160	140	85	75	60	35

Represent this information by fully completing a Venn diagram. [A Venn diagram with three intersecting circles labeled $S$ , $M$ , and $T\,$ is provided. The region for $S\,$ only (sites detected by $S\,$ but not $M\,$ or $T$ ) is marked with the value 95.]

Blank three-set Venn diagram for sensors S, M and T, with 95 given in the S-only region.

A geological site is selected at random from the 400 sites. Calculate the probability that the site:

(i) triggered detection in the Spectrometer only.

(ii) triggered detection in at least two of the sensors.

(iii) triggered detection in the Spectrometer or the Magnetometer (or both), given that it did not trigger the Thermal Imager.

Determine whether the detection of a signature by the Magnetometer and the detection by the Thermal Imager are statistically independent. Justify your answer with numerical evidence.

An automated planetary rover analyzes 400 specific geological sites on Mars. Each site is tested for the presence of specific signatures using three sensors:

Spectrometer ( $S$ )
Magnetometer ( $M$ )
Thermal Imager ( $T$ )

The detection data for these 400 sites is summarized below:

Sensor Detection	$S$	$M$	$T$	$S\,$ and $M$	$S\,$ and $T$	$M\,$ and $T$	All three
Number of Sites	220	160	140	85	75	60	35

Blank three-set Venn diagram for sensors S, M and T, with 95 given in the S-only region.

A geological site is selected at random from the 400 sites. Calculate the probability that the site:

(i) triggered detection in the Spectrometer only.

(ii) triggered detection in at least two of the sensors.

(iii) triggered detection in the Spectrometer or the Magnetometer (or both), given that it did not trigger the Thermal Imager.

Determine whether the detection of a signature by the Magnetometer and the detection by the Thermal Imager are statistically independent. Justify your answer with numerical evidence.

2.3 Conditional Probabilities in Venn Diagrams

Question 20

Markscheme

2.3 Conditional Probabilities in Venn Diagrams

Question 20

Markscheme

2.3 Conditional Probabilities in Venn Diagrams

Question 20

2.3 Conditional Probabilities in Venn Diagrams Questions

2.3 Conditional Probabilities in Venn Diagrams

Question 20

2.3 Conditional Probabilities in Venn Diagrams Questions