Answer:
Figure out the various probabilities first, that will make the rest of the questions easier:
P(discovered) = .7
P(not discovered) = 1 - .7 = .3
P(locator|discovered) = .6
P(no locator|discovered) = 1 - .6 = .4
P(locator|not discovered) = 1 - .9 = .1
P(no locator|not discovered) = .9
P(discovered and locator) = .7 * .6 = .42
P(discovered and no locator) = .7 * .4 = .28
P(not discovered and locator) = .3 * .1 = .03
P(not discovered and no locator) = .3 * .9 = .27
a) The total probability that an aircraft has a locator is .42 + .03 = .45. So the probability it will not be discovered, given it has a locator, is .03/.45 = .067
b) The total probability that an aircraft does not have a locator is .28 + .27 = .55. So the probability it will be discovered, given it does not have a locator, is .28/.55 = .509
c) Probability that 7 are discovered = C(10,7) * P(discovered|locator)^7 * P(not discovered|locator)^3
We already figured out P(not discovered|locator) = .067, so P(discovered|locator) = 1-.067 = .933. C(10,7) = 10*9*8, so we can compute total probability: 10*9*8 * .933^7 * .067^3 = .133
Step-by-step explanation:
