Question

1.) Two regular (six-sided) dice are thrown together. Use a tree diagram to find the probability that one number is even and the other is odd.

2.) The probability that January 1st of a randomly selected year falls on a Monday is 1/7. The probability that January 1st and January 8th of a randomly selected year both fall on a Monday is: a.) 1/49 b.) 0 c.) 1 d.) 1/7 e.) 2/7

3.) In a group of 20 adults, there are eight males and nine Labour supporters. Further, there are five male Labour supporters. What is the probability of randomly selecting a female who does not support Labour? a.) 0.2 b.) 0.5 c.) 0.4 d.) 0.3 e.) 0.6

4.)

An entire week's output of the Christchurch Cool Cone Company was surveyed, and the numbers of acceptable and defective items produced each day were found to be as follows:

	Mon	Tue	Wed	Thu	Fri
Acceptable	135	204	190	153	66
Defective	45	36	60	57	54

A single item is chosen at random from this week's production. Calculate the probability that it is defective, given that it is produced on Tuesday.

Answer 1

1) The tree diagram for the rolls of two dice is given below.

From the diagram we can see that there are a total of ot comes of which outcomes have one number odd and other odd.

So the required probability is

2) If January 1 falls on Monday then January 8 also falls on Monday, since there is a gap of 7 days. So the required probability is sam .

3)Out of 20 adults, 8 are males and 12 are females. 5 males support labor. and 4 females support labour. 8 females do not support labour. So the required probability is

Correct choice is (C).

4) The conditional probability that a randomly selected item is defective, given that it is produced on Tuesday is (consider only Tuesdays data)