Magnetic surveying is one technique used by archaeologists to determine anomalies arising from variations in magnetic susceptibility. Unusual changes in magnetic susceptibility might (or might not) indicate an important archaeological discovery. Letxbe a random variable that represents a magnetic susceptibility (MS) reading for a randomly chosen site at an archaeological research location. A random sample of120 sitesgave the readings shown in the table below.

Magnetic Susceptibility Readings,

centimeter-gram-second10⁶(cmg10⁶)CommentMagnetic

SusceptibilityNumber of

ReadingsEstimated

Probability"cool"0x< 10

3030/120 =0.25"neutral"10x< 20

5454/120 =0.45"warm"20x< 30

1818/120 =0.15"very interesting"30x< 40

1212/120 =0.10"hot spot"40x

66/120 = 0.05

Suppose you are working in a "warm" region in which all MS readings are 20 or higher. In this same region, what is the probability that you will find a "hot spot" in which the readings are 40 or higher? Use conditional probability to estimateP(40x| 20x).

(Round your answer to three decimal places.)

P(40x| 20x)

=