Conditional Probability

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Question 59

A botanical research station monitors a collection of 200 rare orchids for three specific fungal infections. Let $R\,$ be the event that an orchid has root rot, $L\,$ be the event of leaf spot, and $S\,$ be the event of stem rust.

The distribution of infections in the collection is as follows:

18 orchids have only root rot.
14 orchids have only leaf spot.
22 orchids have only stem rust.
7 orchids have root rot and leaf spot but no stem rust.
9 orchids have root rot and stem rust but no leaf spot.
6 orchids have leaf spot and stem rust but no root rot.
4 orchids suffer from all three infections.
The remaining orchids are healthy (free from all three infections).

One orchid is selected at random from the collection.

Determine the probability that the orchid does not have stem rust.

[2]

Find $\cap L \cap S')$ .

[1]

Find $\cup L \cup S')$ .

[2]

Calculate the probability that the orchid has at most one type of infection.

[2]

Given that the selected orchid has at most one type of infection, find the probability it has root rot.

[2]

The random variable $X\,$ represents the number of different types of infections found on a randomly selected orchid.

Find the expected value $E (X)$ .

[2]

Conditional Probability

Question 59

The distribution of infections in the collection is as follows:

18 orchids have only root rot.
14 orchids have only leaf spot.
22 orchids have only stem rust.
7 orchids have root rot and leaf spot but no stem rust.
9 orchids have root rot and stem rust but no leaf spot.
6 orchids have leaf spot and stem rust but no root rot.
4 orchids suffer from all three infections.
The remaining orchids are healthy (free from all three infections).

One orchid is selected at random from the collection.

Determine the probability that the orchid does not have stem rust.

[2]

Find $\cap L \cap S')$ .

[1]

Find $\cup L \cup S')$ .

[2]

Calculate the probability that the orchid has at most one type of infection.

[2]

Given that the selected orchid has at most one type of infection, find the probability it has root rot.

[2]

The random variable $X\,$ represents the number of different types of infections found on a randomly selected orchid.

Find the expected value $E (X)$ .

[2]

Conditional Probability

Question 59

Conditional Probability Questions

Conditional Probability

Question 59

Conditional Probability Questions