Give your answer to 3 decimal places. Fill in the blank: The probability of each

Question

Give your answer to 3 decimal places.
Fill in the blank:
The probability of each pair is: _______ .
Step 1:
Some games of chance rely on tossing two dice. Each die has six faces, marked with 1, 2, . . . , 6 spots called pips. The dice used in casinos are carefully balanced so that each face is equally likely to come up. When two dice are tossed, each of the 36 possible pairs of faces is equally likely to come up. The outcome of interest to a gambler is the sum of the pips on the two up-faces. Call this random variable .

If all pairs have the same probability, what must be the probability of each pair (assuming that we distinguish between, e.g., (1,2) and (2,1))? Give your answer to 3 decimal places.
Fill in the blank:
The probability of each pair is: _______ .






Step 2:
Some games of chance rely on tossing two dice. Each die has six faces, marked with 1, 2, . . . , 6 spots called pips. The dice used in casinos are carefully balanced so that each face is equally likely to come up. When two dice are tossed, each of the 36 possible pairs of faces is equally likely to come up. The outcome of interest to a gambler is the sum of the pips on the two up-faces. Call this random variable .

One bet available in craps wins if a 7 or an 11 comes up on the next roll of two dice. What is the probability of rolling a 7 or an 11 on the next roll?
Give your answer to 3 decimal places.
Fill in the blank:
_______ .

Explanation / Answer

Step 1)

There are total 36 outcomes ( 36 possible pairs of faces ). Each pair is unique and equally likely to happen.

therefore probability of occurance of each pair = 1/36=0.028

Step 2) Pair that can give us a total of 7 = (1,6), (6,1), (2,5), (5,2), (3,4), (4,3) =6

             Pair that can give us a total of 11= (5,6), (6,5) =2

P(X=7) = 6/36 = 0.167

P(X=11) = 2/36 = 0.056

P(X=7 or X=11) = P(X=7) + P(X=11) = 0.167 + 0.056 =0.223

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