Question

The table below shows whether students from a certain University in Pretoria are right- or left- handed by sex. The total number of students who were interviewed was 100. Their responses were as follows:

    Right handed Male Female Total

38 42 80

Left handed 12 8 20

Total 50 50 100

      3.1.1 What is the probability of selecting a left-handed male?

3.1.2 What is the probability of selecting a right-handed female?

3.2 A construction firm has bid on two different contracts. Let B1 be the event that the first bid is successful and B2, that the second bid is successful. Suppose that P (B1) = .4, P (B2) = .6 and that the bids are independent. What is the probability that:

3.2.1. Both bids are successful?

3.2.2. Neither bid is successful?

Answer 1

3.1

1. P(left-handed male) $= \frac{Left-hunded \;male}{Total}$

$= \frac{8}{100} \\ = 0.08$

2. P(right-handed female) $= \frac{Right-hunded \;female}{Total}$

$= \frac{42}{100} \\ = 0.42$

3.2

P(B1) = 0.4

P(B2) = 0.6

3.2.1. Both bids are successful

P(B1 and B2) $= 0.4 \times 0.6 = 0.24$

3.2.2. Neither bid is successful

P(not B1 and not B2) = (1 – P(B1)) (1 – P(B2))

$= 0.6 \times 0.4 = 0.24$