Question

A single die is rolled 19 times. What is the probability that a five is rolled exactly once, if it is known that at least one five is rolled? |

Answer #1

If a single six-sided die is rolled five times, what is the
probability that a six is thrown exactly three times?
a)
0.125
b)
0.032
c)
0.042
d)
0.5

A fair 4-sided die is rolled 7 times.
(a)
Find the probability that the side 1 comes up exactly 3
times.
(b)
Find the probability that there is at least one side that comes
up exactly 3 times.

A single die is rolled ten times. Find the probability that 3
appears at most three times.

1) A fair die is rolled 10 times. Find an expression for the
probability that at least 3 rolls of the die end up with 5 dots on
top.
2) What is the expected number of dots that show on the top of
two fair dice when they are rolled?

A die is rolled 300 times; it lands five 58 times. Is this
evidence significant enough to conclude that the die is not fairly
balanced (alpha is 0.05)? ....Continuing the previous die problem,
suppose that the true chance of landing five is 0.25. Draw the
picture to state the region of , which is the probability of making
the Type II error.

a single die is rolled one time, what is the probability of
rolling a number greater than 1 and less than 4

a fair die is rolled 8 times what is the probability
that not more that 2 sixes come up.

A fair die is rolled five times.
(a) Compute the joint p.m.f. of X and Y , where X is the first
number rolled and Y is the largest of the five numbers rolled.
(b) Compute the joint p.m.f. of X and Y , where X is the first
number rolled and Y is the number of 1’s rolled.

Assume that a fair
six-sided die is rolled 9 times, and the roll is called a success
if the result is in {1,2}{1,2}.
What is the probability that there are exactly 4 successes or
exactly 4 failures in the 9 rolls?

A die is rolled 8 times, what is the probability that the sum of
the numbers that comes up is 33?
Start:
x1+x2+...+x8=33; 1<=xi<=6
C1: x1>=7 S_0 = (40C7)
C2: x2>=7 S_1 = N(C1) + N(C2) +...+N(C8)
.
.
C8: x8 >=7

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