MDM 4U
Chapter 4_Answer Section
1.A permutation should be used because order matters in this case.
2.If they are disjoint, they do not have any common elements and these common elements do not need to be subtracted.
- If the team wins a game, it gains confidence and the probability of the team winning its next game increases. If the team loses a game, its confidence goes down and the probability of the team winning its next game decreases. The probability of a team winning its next two games is the product of the probability that it will win its next game multiplied by the probability of it winning its second game given that it has won its first. This second probability will be more than 0.5 because it has gained confidence. Therefore, the probability of the team winning its first game must be more than (0.5)(0.5) = 0.25.
4. P(Larry wins at least two games) / = P(Larry wins games 1 and 2)
+ P(Larry wins games 1 and 3)
+ P(Larry wins games 2 and 3)
+ P(Larry wins all 3 games)
= (0.4)(0.5)(0.4) + (0.4)(0.5)(0.45) + (0.6)(0.35)(0.45)
+ (0.4)(0.5)(0.6)
= 0.3845
6.
7.Number of ways = (total number of ways) (number of ways with zero bars with nuts) (number of ways with 1 bar with nuts)
8.Let be the event that both students selected are girls ; be the event that at least one student selected is a girl.
9. The number of ways to choose two face cards is C(12, 2) = 66 and the number of ways to choose consecutive cards is (4 suits)(12 pairs of consecutive cards) = 48. However, the Jack and Queen and Queen and King are examples of both of these situations, and there are 8 of these possibilities. Thus, the number of ways to win is 66 + 48 8 =106. The number of ways to choose 2 cards in total is C(52, 2) = 1326. Thus, the probability of winning the game is and the number of wins in 50 games is approximately. Therefore, the winnings would be 4($2.00)=$8.00.
10.P(sum of eight or doubles) = P(sum of eight) + P(doubles) P(sum of eight and doubles)
11.P(tails and an ace and an even number) 12. P(DVD, poster, DVD)
P(this happens three times)
13.P(two of the three names chosen are from the same grade):
15. P(owning a racing or mountain bike) = P(owning a racing bike) + P(owning a mountain bike) P(owning both)
Therefore, P(owning neither)
16.
17. The value of P(A) is .
18.The probability that the marble is yellow if it is known that is not green is 0.125.
19.
20. The number of ways is 10 080.
21. The probability of the order red, red, purple, green is .
- The probability that F is the first letter and Y the last is .
23. The number of ways that this could be done is 60 060.