In this worksheet, we will practice using theoretical and experimental probabilities to calculate expected values.

**Q1: **

How many times would you expect a prime number to occur if a fair die were rolled 300 times?

**Q3: **

The table shows the results of rolling a die 78 times. Using this information, how many times is the number 2 expected to appear if the die is rolled 234 times?

Number | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|

Rolls | 23 | 17 | 15 | 10 | 2 | 11 |

**Q5: **

The probability that a biased die will land on an even number is 0.6. If the die is rolled 80 times, how many times is it expected to land on an even number?

**Q6: **

A factory produced 1 600 calculators in one day. They took a sample of those calculators and found that were defective. What is the expected number of defective calculators produced that day?

**Q7: **

A factory produced 2 000 light bulbs each day. A sample of 500 bulbs were tested and 29 of them were defective. What is the expected number of non-defective bulbs produced in a day?

**Q8: **

A factory produces 8,000 shirts each day. At the end of a day, 1,600 shirts were inspected and 50 were found to be defective. What is the expected number of defective shirts produced that day?

**Q9: **

A factory produces two types of shirts: A and B. The table shows how many shirts of each type were sold in 5 samples of 100 shirts from 5 different shopping malls.

Shopping Mall | (1) | (2) | (3) | (4) | (5) |
---|---|---|---|---|---|

Sales of Type A | 35 | 66 | 29 | 44 | 53 |

Sales of Type B | 65 | 34 | 71 | 56 | 47 |

If the factory sells 3,000 shirts, how many of them do you expect to be of type A?

**Q10: **

In a survey of 400 tourists who visited Egypt, 160 were from Arab countries, 120 were from Europe, 40 from Latin America, and 80 from Australia. If the total number of tourists who visited Egypt in a month was 5,000, how many of them are expected to be from Europe?