S.aux.26 our-sided die has three blue faces, and one red face.......

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In summary, a four-sided die has three blue faces and one red face. When rolled, the probability of a blue face landing down is 3/4 and the probability of a red face landing down is 1/4. In a game played with this die, if the blue face lands down, the game ends and the player scores 2. If the red face lands down, the player scores 1 and rolls the die again. Let X be the total score obtained in this game. The probability of obtaining a total score of 3 is 3/16, and the probability of obtaining a total score of 2 is 13/16. The expected value of X is 2 and 3/16. If
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karush
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four-sided die has three blue face, and one red face.
The die is rolled.
B be the event blue face lies down, and R be the event a red face lands down
a Write down
i $\quad P(B)=\dfrac{3}{4}\quad$ ii $\quad P(R)=\dfrac{1}{4}$

b If the blue face lands down, the dieu is not rolled again. If the red face lands down, the die is rolled once again.
This is represented by the following tree diagram, where p, s, t are probabilities.

276.png


Find the value of p, of s and of t.

c Guiseppi plays a game where he rolls the die.
If a blue face lands down, he scores 2 and is finished.
If the red face lands down, he scores 1 and rolls one more time.
Let X be the total score obtained.
$ \quad \texit{
Show that } $P(X=3)=\frac{3}{16}$
[ii] Find $\quad P(X=2)$

[d i] Construct a probability distribution table for X. [5 marks]
[ii] Calculate the expected value of X.

[e] If the total score is 3, Guiseppi wins . If the total score is 2, Guiseppi gets nothing.
Guiseppi plays the game twice. Find the probability that he wins exactly .

ok I only time to do the first question so hope going in right direction
I know the answers to all this is quickly found online but I don't learn too well by C/P
 
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a) Yes, the probability of Blue on one roll is 3/4 and the probability if Red is 1/4.

b) On the diagram, p is obviously 3/4. q is (1/4)(3/4)= 3/16. r is (1/4)(1/4)= 1/16.
(Note that 3/4+ 3/16+ 1/16= 1.)

c) The probability of Blue is 3/4 and gives a value 2, The probability of Red, Blue is 3/16 and gives a value 1+ 2= 3. The probability of Red, Red is 1/16 and gives a value 1+ 1= 2. So P(X= 2) is 3/4+ 1/16= 12/16+ 1/16= 13/16. P(X= 3) is 3/16.

di) Since 2 and 3 are the only possible values for X, P(X= 2)= 13/16, P(X= 3)= 3/16 IS the "probability distribution table" for X. (And of course 13/16+ 3/16= 16/16= 1.)

dii) The expected value is (3/4)(2)+ (3/16)(3)+ (1/16)(2)= 24/16+ 9/16+ 2/16= 35/16= 2 and 3/16.

e) The probability Giussepe loses both games is (13/16)(13/16)= 169/256. The probability Giussepe wins one game and losess the other is (13/16)(3/16)+ (3/16)(13/16)= 78/256. The probability Giussepe wins both games is (3/16)(3/16)= 9/256. (Once again, observe that 169/256+ 78/256+ 9/256= 256/256= 1.)
 
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  • #3
Mahalo
that was a great help
ill try the next one all the way thru
 

FAQ: S.aux.26 our-sided die has three blue faces, and one red face.......

1. What is the probability of rolling a blue face on the S.aux.26 four-sided die?

The probability of rolling a blue face on the S.aux.26 four-sided die is 3 out of 4, or 75%. This is because there are three blue faces out of a total of four faces on the die.

2. What is the probability of rolling a red face on the S.aux.26 four-sided die?

The probability of rolling a red face on the S.aux.26 four-sided die is 1 out of 4, or 25%. This is because there is only one red face out of a total of four faces on the die.

3. How many possible outcomes are there when rolling the S.aux.26 four-sided die?

There are four possible outcomes when rolling the S.aux.26 four-sided die. These outcomes are rolling a blue face, rolling a red face, rolling a blue face twice in a row, and rolling a red face twice in a row.

4. Is the S.aux.26 four-sided die fair?

No, the S.aux.26 four-sided die is not fair. This is because there are three blue faces and only one red face, giving a higher probability of rolling a blue face compared to a red face.

5. How does the S.aux.26 four-sided die compare to a traditional six-sided die?

The S.aux.26 four-sided die is different from a traditional six-sided die in terms of the number of faces and the probabilities of rolling each face. The traditional six-sided die has an equal probability of rolling each face, while the S.aux.26 four-sided die has a higher probability of rolling a blue face compared to a red face.

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