1.A number cube labeled with numbers 1, 2, 3, 4, 5, and 6 is tossed. What are th

Question

1.A number cube labeled with numbers 1, 2, 3, 4, 5, and 6 is tossed. What are the odds for the cube showing a number less than 3?  

2.The odds against Chip beating his friend in a round of golf are 1 : 8. Find the probability that Chip will beat his friend.

3.If two fair dice are rolled, what is the probability that a total showing is either even or less than eight?

4.Suppose two cards are drawn from a well-shuffled deck of 52-cards. What is the probability that both cards are face cards?

Write the answer as a percentage rounded to the nearest tenth of a percent.

Explanation / Answer

(1)

Total number of outcomes = 6

Number of outcomes that show less than 3 = 2.

So, The odds for the cube showing a number less than 3 = 2/6 = 1/3 = 0.3333

(2) Odds against Chip beating his friend = 1/8

So,

Odds in favour of Chip beating his friend = 1 - 1/8 = 7/8 = 0.8750

So,

Probability that Chip will beat his friend = 0.8750

(3) Total number of outcomes = 36

Total showing even:

(1,1),(1,3),(1,5) - 3 Nos.

(2,2), (2,4), (2,6) - 3 Nos.

(3,1), (3,3), (3,5) - 3 Nos.

(4,2), (4,4), (4,6) - 3 Nos

(5,1), (5,3), (5,5) - 3 Nos.

(6,2), (6,4), (6,6) - 3 Nos.

Total                    = 18

So,

P(total even) = 18/36 = 0.5

Total less than 8:

(1,1), (1,2), (1,3), (1,4),(1,5), (1,6) - 6 Nos.

(2,1), (2,2), (2,3) (2,4), (2,5)        - 5 Nos.

(3,1), (3,2), (3,3), (3,4)            - 4 Nos.

(4,1), (4,2), (4,3)                    - 3 Nos.

(5,1), (5,2)                             - 2 Nos.

(6,1)                                     - 1 No.

Total                                = 21

So,

P(Total less than 8) = 21/36 = 0.5833

Total even & Total less than 8:

(1,1), (1,3), (1,5) - 3 Nos.

(2,2), (2,4)         - 2 Nos

(3,1), (3,3)          - 2 Nos.

(4,2)                 - 1 No.

(5,1)                 - 1 No

------------------------------------

Total                   9 Nos.

So,

P(Total even & Total less than 8) = 9/36 = 0.25

By Addition Theorem:

P(Total evn OR less than 8) = 0.5 + 0.5833 - 0.25 = 0.8333

(4)

Total number of cards = 52

Number of face cards = 12

P(first cand is face card) = 12/52 = 0.2308

After first draw:
Total number of cards = 51

Number of face cards = 11

So,

P(Second card is face card)= 11/51 = 0.2157

So,

P(both cards are face cards) = 0.2308 X 0.2167 = 0.0498

So,

Answer is:    4.98%

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