Answer to Question #167152 in Statistics and Probability for mandie sun

Question

From past experience, an oil exploration company knows that each new well drilled has a 32% chance of being viable for oil production. The company is planning to drill five new wells. Assume that all wells are independent.

(a) What is the probability that the first well will not be viable?

(b) What is the probability that none of the five wells will be viable?

(c) What is the probability that at least one of the five wells will be viable?

Answer 1

Probability that a well being viable $p=\dfrac{32}{100}=0.32$

Probability that well not be viable $q=1-p=1-0.32=0.68$

Here n=5

(a)Probability that first well will not be viable= $1-P(\text{ first well is viable})$

$=1-^5C_1(0.32)^1(068)^4$

$=1-0.342=0.658$

(b) Probability none of the wells is viable = $^5C_0(0.32)^0(0.68)^5=0.1454$

(c) Probability that at lest one well is viable = 1-P( none of the wells is viable)

$=1-0.1454=0.8546$