Two fair dice are rolled 4 times and the sum of the numbers that come up are recorded. find the probability of these events. a) the sun is 5 on each of the four rolls. b) the sun is 5 exactly three times in the four rolls.

See below in bold.

Step-by-step explanation:

A.  On one roll the possible ways to get a sum of 5 is (2,3, ) and (4, 1).

There are 36 possible outcomes from the one roll of the 2 dice.

So the probability of getting  a sum of 5 on one roll =  2/36 = 1/18.

So the probability of 5 on 4 rolls = (1/18)^4

= 1/104976.

B.  

The probability of the first 3 rolls being a 5 and the last one being not 5

= (1/18)^3 * (17/18)

= 17/104976

There are 4 ways to  pick 3 out of 4 so the required probability

=  4 * 17/104976

= 68/104976.

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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he sells x mount because thats eqivilqant to the maz and then divided into quarters

step-by-step explanation: