A fair die is rolled n times. Let An be the event that there is a string of k consecutive rolls among n rolls in which all upturned faces are number 6. Compute P(An). Here we assume that the rolls are independent with each other and 0 < k < n. Note that, to reduce your overload, you only need to derive the recursion formula , i. e., you DO NOT need to solve that recursion formula.

the answer is 24

step-by-step explanation:

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step-by-step explanation:

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560

investment b is an ordinary annuity with $3,909.64 in the account after one year.

step-by-step explanation: