**QUESTION ONE (30 MARKS)**

- What is the probability that a card drawn at random from a deck of cards will be an ace? (4)
- What is the probability that the total of two dice will be greater than 9 given that the first die is a 6? (4)
- Someone draws a card at random out of a deck, replaces it, and then draws another card at random. What is the probability that the first card is a “3” and the second card is a Diamond? (4)
- If someone draws a card at random from a deck and then, without replacing the first card, draws a second card, what is the probability that the 1st card is an Ace and the second card is a 10? (4)
- What is the probability of rolling a die and getting either a 2 or a 3? (4)
- What is the probability that a card selected from a deck will be either a “10” or a Diamonds? (4)
- How many ways can you arrange 12 books if you have space for 6 books in your bookcase? (3)
- How many different groups of 4 can be selected from 12 people? (3)

**QUESTION TWO (30 MARKS)**

In the mid-1990s, time magazine reported that 27% of the US Congress supported a tax cut as a means of stimulating the economy and increasing Tax revenues. Suppose at that time five members of congress were randomly selected for an interview and asked whether they supported the tax cut to stimulate the economy.

Find the probability that:

- At least three of the five members were in favour of a tax (6)
- Less than five members were in favour of a tax (6)
- Not more than 3 members were in favour of the (6)
- Find the mean of the above distribution (6)
- Find the variance and standard deviation of the above distribution (6)

**QUESTION THREE (30 MARKS)**

3.1 A consumer group has tested five makes of certain brand. The prices and the scores (out of 100) awarded to them by a panel of experts are as follows:

PRICE (X) | SCORE (Y) |

95 | 74 |

69 | 63 |

18 | 28 |

32 | 33 |

27 | 37 |

Using the data provide above to calculate the following:

- Pearson’s correlation (r) (15)
- Spearman’s correlation (𝜌) (15)

**Answers to Above Statistics Questions**

- The probability that a card drawn at random from a deck of cards will be an ace is calculated as follows:

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