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Chapter 5: Q T5.11. (page 337)

Your teacher has invented a 鈥渇air鈥� dice game to play. Here鈥檚 how it works. Your teacher will roll one fair eight-sided die, and you will roll a fair six-sided die. Each player rolls once, and the winner is the person with the higher number. In case of a tie, neither player wins. The table shows the sample space of this chance process.

(a) Let A be the event 鈥測our teacher wins.鈥� Find P(A).

(b) Let B be the event 鈥測ou get a 3 on your first roll.鈥� Find P(A 鈭� B).

(c) Are events A and B independent? Justify your answer.

Short Answer

Expert verified

Part (a) The probability is 0.5625

Part (b) The probability is 0.625

Part (c) No.

Step by step solution

01

Part (a) Step 1. Given

The table is

02

Part (a) Step 2. Concept used

Probability=FavourableoutcomesTotaloutcomes

03

Part (a) Step 3. Calculation

The teacher is victorious in event A.

In 1+2+3+4+5+6+6=27situations, the teacher will win.

There are 48 examples in total.

P (A) is computed as:

P(A)=2748=0.5625

Thus, P(A)=0.5625

04

Part (b) Step 1. Calculation

The event B indicates that on the first roll, a 3 will be achieved.

P(A鈭�B) is computed as:

P(A鈭�B)=P(A)+P(B)鈭�P(A鈭�B)

P(A鈭�B)=2748+848-548=3048=0.625

Thus, the probability is 0.625

05

Part (c) Step 1. Calculation

P(A)=2748P(B)=848P(C)=548

The following conditions must be met for the occurrences to be independent:

P(A鈭�B)=P(A)脳P(B)2748脳748=5482162304isnotequalto548

Because the preceding criteria are not met, A and B are not independent events.

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