Assume that you have two dice, one of which is fair, and the other is biased toward landing on six, so that 0.25 of the time it lands on six, and 0.15 of the time it lands on each of 1, 2, 3, 4 and 5. you choose a die at random, and roll it six times, getting the values 4, 3, 6, 6, 5, 5. what is the probability that the die you chose is the fair die? the outcomes of the rolls are mutually independent.

0.4038

Step-by-step explanation:

Let A and B be the events

A: “The die is fair”

B: “The die lands on 6 two times out of 6”

We want to determine if the die is fair given that it landed on 6 two times out of 6 tosses, that is P(A | B).

By the Bayes' theorem  

Where is the event “the die is not fair”.

Since there are 2 dice,

If the die is fair P(B | A) is the probability of getting exactly two six in a binomial experiment with probability of “success” (land on 6) 1/6 and six repeated trials  

and is the probability of getting exactly two six in a binomial experiment with probability of “success” (land on 6) 0.25 and six repeated trials  

hence

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.

what statement? is there an image?