On his university application, Prashad must list his course choices in order of preference.

Question 1:

On his university application, Prashad must list his course choices in order of preference.

He must choose four of the six courses available in his major discipline and three of the four courses offered in related subjects.

In how many ways can Prashad list his course choices? Explain the reasoning for your answer.

He can select his major by selecting any four of the six courses available and as the order does not matter so the required number of ways to do such = 6C4 = 15.

Now for each of these 15 ways he can select any 3 out of the 4 courses offered in related subjects so the total number of ways = 15*4C3 = 15*4 =60

Question 2:

During a recent survey of ethnic backgrounds of 1000 people in a large city, 513 were Canada, 148 were French 72 were African and 56 were Asian and the remainder were from other groups. Calculate the probability that a person, selected at random from the population has:

a Canadian background?

= Number of people with Canadian background / total number of people

= 513/1000 = 0.513

an African background?

= Number of people with African background / total number of people

= 72/1000 = 0.072

an “other” background?

= Number of people with “other” background / total number of people

= (1000-513-148-72-56)/1000

= 211/1000 = 0.211

Question 3:

Use a tree diagram to explain why the probability that a family with four children has either all four children of the same gender is 1/8. Assume that the probability of having a girl is equal to the probability of having a boy. 

The required tree diagram is given below,

Thus required probability = P(All are girls) + P(All are boys)

= 0.0625+0.0625

= 0.125 or 1/8