For a probability distribution the expected value is the summation of product of probabilities with their respective data values. Let x be the probability that Jackson goes gym for 2 days and y be the probability that he goes gym for 3 days.
For the given case we have following values and their probabilities:
0 : 0.1
2 : x
3 : y
So the expected value will be = 0(0.1) + 2(x) + 3(y)
Expected value is given to be 2.05. So we can write the equation as:
2x + 3y = 2.05 (Equation 1)
Also for a probability distribution, the sum of probabilities must always equal to 1. So we can set up the second equation as:
0.1 + x + y = 1
x + y = 0.9 (Equation 2)
From Equation 2 we can write the value of x to be x = 0.9 - y. Using this value in equation 1, we get:
2(0.9 - y) + 3y = 2.05
1.8 - 2y + 3y = 2.05
1.8 + y = 2.05
y = 0.25
Using the value of y in equation 2 we get value of x to be 0.65
Therefore we can conclude that:
The probability that Jackson goes to gym for 2 days is 0.65 and the probability that he goes to gym for 3 days is 0.25
<span>45% -------------------------------chance that the land has oil
then
55</span>%--------------------------------chance that the land not have oil
<span>80% -------------------accuracy rate of indicating oil in the soil. (if land does have oil)
20</span>% -------------------accuracy rate of indicating not oil in the soil. (if land does have oil)
20% ---------------------accuracy rate of indicating oil in the soil. (if land has not oil)
80% ---------------------accuracy rate of indicating not oil in the soil. (if land has not oil)
that the land has no oil----------------55%
the test shows that it has oil-------- 20%
then 0.55*0.20=0.11=11%
the probability that the land has no oil and the test shows that it has oil is 11%
