An experiment consists of rolling a weighted die. The probability of rolling each number is: Pr[1]=0.05Pr[1]=0.05, Pr[2]=0.25Pr[2]=0.25, Pr[3]=0.1Pr[3]=0.1, Pr[4]=0.15Pr[4]=0.15, Pr[5]=0.2Pr[5]=0.2, and Pr[6]=0.25Pr[6]=0.25. On the first roll, you record if the number is Small (1,2) or Large (3,4,5,6). If the first number is Small, then on the second roll you record if the number is a 1 or not. If the first number is Large, on the second roll you record whether the number is Small or not. So, some typical outcomes would be S1 (small number rolled, then 1) or LL (large number rolled, then another large number). Draw a tree diagram and use it to answer the following questions.(1) What is Pr[S1]?(2) What is Pr[LL]? (3) What is Pr[(not1)onsecondroll|Sonfirstroll]?(4) What is Pr[S on second roll|L on first roll]?

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Asked Feb 14, 2020
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An experiment consists of rolling a weighted die. The probability of rolling each number is: Pr[1]=0.05Pr[1]=0.05, Pr[2]=0.25Pr[2]=0.25, Pr[3]=0.1Pr[3]=0.1, Pr[4]=0.15Pr[4]=0.15, Pr[5]=0.2Pr[5]=0.2, and Pr[6]=0.25Pr[6]=0.25. On the first roll, you record if the number is Small (1,2) or Large (3,4,5,6). If the first number is Small, then on the second roll you record if the number is a 1 or not. If the first number is Large, on the second roll you record whether the number is Small or not. So, some typical outcomes would be S1 (small number rolled, then 1) or LL (large number rolled, then another large number). Draw a tree diagram and use it to answer the following questions.

(1) What is Pr[S1]?

(2) What is Pr[LL]? 

(3) What is Pr[(not1)onsecondroll|Sonfirstroll]?

(4) What is Pr[S on second roll|L on first roll]?

 

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Step 1

The tree diagram for the given information is drawn as follows:

Probability homework question answer, step 1, image 1

It is given that,

Probability homework question answer, step 1, image 2

Step 2

Consider,

Probability homework question answer, step 2, image 1

 

Step 3

1).

The probability of the event P(S1) is calculated as follows:

Probability homework question answer, step 3, image 1

2).

The probability of the event P(LL) is calculated as follows:

Probability homework question answer, step 3, image 2

...

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