a) flipping 2 counters, Cam's outcomes:
11 , 12 , 21, and 22 , two ways to get a 3
---> prob(3) = 2/4 = 1/2
flipping a die, outcomes
1,2,3,4,5,6 , one way to get a 3 --> prob(3) = 1/6
prob(both get a 3) = (1/2)(1/6) = 1/12
CA DE ---- Cam's loss ---> Dean's win
11 3,4,5,6,----- 4ways
12 4,5,6--------3ways
21 4,5,6--------3ways
22 5,6 ---------2ways
There are 12 ways for Dean to win
CA DE --- Cam's wins
11 1
12 1,2
21 1,2
22 1,2,3 -------a total of 8 ways
CA DE --- it's a tie
11 2
21 3
12 3
22 4 ------ 4 ways
Prob(Dean wins) = Prob(Cam loses) = 12/24 = 1/2
prob(Cam wins) = 8/24 = 1/3
prob(tie) = 4/24 = 1/6
(note: 1/2 + 1/3 + 1/6 = 1 )
b) repeat experiment
Cam and Dean are playing a game with counters and dice. Cam has some counters, each labelled 1 on one side and 2 on the other. He flips the counters and scores the total of all the numbers showing. Dean has one die and scores the number showing after he rolls it. The winner is the player with the higher score. The game is a draw if both scores are the same. All counters and dice are fair, that is, all faces are equally likely to come up.
a) Cam flips 2 counters while Dean rolls one 6 faced die.
i) Calculate the probability that both score 3 in a game. (Correct probability)
ii) Explain why Cam is more likely to lose. (Convincing explanation)
b) Who is more likely to win if Cam flips three counters while Dean rolls one normal die? (Correct person with explanation)
c) Dean rolls an octahedral die with faces labelled 1 to 8. Determine the number of counters Cam must flip to make this a fair game, that is, a game in which Cam and Dean have same chance of winning. (Correct number of counters with explanation)
3 answers
You shouldn't be asking for help in the maths challenge. It is against the rules.
Cheater! I am doing the maths challenge too and this isn't fair to the other students.
1 answer