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.

c = 0.429t

step-by-step explanation:

the constant rate at which carlos harvests cassava is 35 minutes per 15 cassavas 15/35 = 0.429 cassava per minute

therefore, an equation that models the number of cassava (c) that harvest carlos in a time (t) is the following:

where t is the time in minutes.

this means that when 35 minutes have elapsed 15 cassava have been harvested, at 70 minutes 30 cassava have been harvested and so on.

13664

step-by-step explanation:

=cross multiply

=100 x = 13664