A die is weighted in such a way that each of 2, 4, and 6 is twice as l

rescuedbyhimw0

rescuedbyhimw0

Answered question

2021-11-18

A die is weighted in such a way that each of 2, 4, and 6 is twice as likely to come up as each of 1, 3, and 5. Find the probability distribution and find the probability of rolling less than 3. 
Outcome123456Probability 

Answer & Explanation

Knes1997

Knes1997

Beginner2021-11-19Added 11 answers

The outcomes for a die are 1, 2, 3, 4, 5 and 6. A die is weighted in such a way that each of 2, 4, and 6 is twice as likely to come up as each of 1, 3, and 5. 
Let us define the probability of getting any of 1, 3 or 5 as p. Hence, the probability of getting 2, 4 or 6 is 2p. 
i=16P(x)=1 
p+2p+p+2p+p+2p=1 
9p=1 
p=19 
The probability distribution function: 
Outcome123456Probability192919291929 
The probability of rolling less than 3: 
P(less than 3)=P(1)+P(2) =19+29 =39 =13 , answer

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