Aux 26 our-sided die has three blue face, and one red face.

[karush]

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
P(B)=\dfrac{3}{4}
P(R)=\dfrac{1}{4}

b If the blue face lands down, the die 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.

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.
i Show that $P(X=3)=\frac{3}{16}$
ii \quad Find $P(X=2)$

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 aswers to all this is quickly found online but I don't learn too well by C/P

 

[jvicens]

a) P(B) = probability of blue face landing down = 3/4
P(R) = probability of red face landing down = 1/4

b) p = probability of scoring 2 if blue face lands down = 1
s = probability of scoring 2 if red face lands down = 1/4
t = probability of scoring 1 if red face lands down = 3/4

c) i) P(X=3) = P(B) + P(R) * P(B) = 3/4 + (1/4 * 3/4) = 3/4 + 3/16 = 9/16 = 0.5625

ii) P(X=2) = P(R) * P(R) = (1/4) * (1/4) = 1/16 = 0.0625

d) i) Probability distribution table for X:

| X | Probability |
|---|-------------|
| 2 | 3/16 |
| 3 | 9/16 |
| 4 | 1/16 |

ii) Expected value of X = (2 * 3/16) + (3 * 9/16) + (4 * 1/16) = 1.75

e) Probability of winning exactly once = P(X=3) = 9/16 = 0.5625