Question

In a basket of 20 apples, there are two rotten apples, 10 good apples, and 8 unripe apples. An apple is drawn 10 times with replacement, and the results are recorded as follows.The number of times rotten apples are selected = 4The number of times good apples are selected = 4The number of times unripe apples are selected = 2Find the expected value.56.20.80.95

Answer 1

Step 1

State the formula for the expected value

`\sum ^{}_{}(x)=\sum ^{}_{}x_iP(x_i)`

Step 2

Find the probabilities

`\text{Probability of rotten apples= }(4)/(10)=0.4`
`\begin{gathered} \text{Probability of good apples=}(4)/(10)=0.4 \\ \text{Probability of unripe apples=}(2)/(10)=0.2 \end{gathered}`

Step 3

Draw up the table

Hence, the expected value = 6.4