Question

IS ANYONE GOOD AT PROBABILITY????
An water well is to be drilled in the desert where the soil is either rock, clay or sand. The probability of rock P(R) = 0.53. The clay probability is P(C) = 0.21. The sand probability is P(S) = 0.26. It if it rock, a geological test gives a positive result with 35% accuracy. If it is clay, this test gives a positive result with 48% accuracy. The test gives a 75% accuracy for sand. Given the test is positive, what is the probability that soil is rock, P(sand | positive)?

Answer 1

is it P(sand |positive) or P(rock |positive) ?

Answer 2

P(sand |positive

Answer 3

in general
\[P(A |B) = \frac{P(AandB)}{P(B)}\]

Answer 4

conditional probability

Answer 5

i have gotten there but now i am stuck :(

Answer 6

not sure what do do now ?

Answer 7

there are 2 missing parts you need to determine
P(sand and positive)
P(positive)

for 1st part...multiply the probabilities
P(sand and positive) = 0.26*0.75

for 2nd part...sum up all possible cases where its positive
P(positive) = P(sand and positive) +P(clay and positive) +P(rock and positive)

Answer 8

so sum of( .53*.35)+(.21*.48)+(.26*.75)