The probability that an archer hits her target when it is windy is 0.4; when it is not windy, her probability of hitting the target is 0.7. On any shot, the probability of a gust of wind is 0.3. Find the probability that:a. On a given shot there is a gust of wind and she hits her target. b. She hits the target with her first shot. c. She hits the target exactly once in two shots. d. There was no gust of wind on an occasion when she missed.

Step-by-step explanation:

Let T be the event that she hot the target and W be the event that there was a gust of wind.

P(T | W) = 0.4

P(T | W') = 0.7

P(W) = 0.3

P(W') = 1 - 0.3 = 0.7

a) P(W T) = P(W) x P(T | W)

= 0.3 x 0.4

= 0.12

b) P(T) = P(W T) + P(W' T)

= 0.12 + 0.7 x 0.7

= 0.61

c) P(she hits the target exactly once in two shots) = P(hits the target on first shot and misses on the second) + P(misses the target on first shot and hits on the second)

= 0.61 x (1-0.61) + (1-0.61) x 0.61

= 0.4758

d) P(W' | T') = P(T'W')/P(T') [Bayes' theorem]

= [0.7 x (1-0.7)]/[0.7 x (1-0.7) + 0.3 x (1-0.4)]

= 0.5385

his chances of getting a coin of higher value is 4/19

step-by-step explanation:

$4034.40

the perimeter of the field is the sum of the lengths of the four sides:

47 yd + 158 yd + 47 yd + 158 yd = 410 yd

the cost of 3 ft (1 yd) of fence is 3×$3.28 = $9.84.

so the cost of jake's wood perimeter fance is

(410 yd) × ($9.84 /yd) = $4034.40