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

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In summary, a four-sided die has three blue faces and one red face. The die is rolled and the probabilities of the blue and red faces landing down are 3/4 and 1/4, respectively. When the blue face lands down, the die is not rolled again. When the red face lands down, the die is rolled once more. The values of p, s, and t are 1, 1/4, and 3/4, respectively. Guiseppi plays a game with this die where he scores 2 if the blue face lands down and 1 if the red face lands down. Let X be the total score obtained. The probability of X = 3 is 9/16
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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
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.

output-onlinepngtools.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.
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
 
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  • #2
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
 

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

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

The probability of rolling a blue face on the aux 26 our-sided die is 3/26 or approximately 11.54%. This is because there are three blue faces out of a total of 26 faces on the die.

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

The probability of rolling a red face on the aux 26 our-sided die is 1/26 or approximately 3.85%. This is because there is only one red face out of a total of 26 faces on the die.

3. What is the probability of rolling a blue face twice in a row on the aux 26 our-sided die?

The probability of rolling a blue face twice in a row on the aux 26 our-sided die is (3/26) x (3/26) = 9/676 or approximately 1.33%. This is because the outcomes of each roll are independent, so the probabilities can be multiplied together.

4. What is the probability of rolling a red face on the first roll and then a blue face on the second roll on the aux 26 our-sided die?

The probability of rolling a red face on the first roll and then a blue face on the second roll on the aux 26 our-sided die is (1/26) x (3/26) = 3/676 or approximately 0.44%. This is because the outcomes of each roll are independent, so the probabilities can be multiplied together.

5. How many different outcomes are possible when rolling the aux 26 our-sided die?

There are 26 different outcomes possible when rolling the aux 26 our-sided die. This is because there are 26 faces on the die, each with a unique color and number combination.

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