Probability 1. Find the probability of each outcome when a biased die is rolled if rolling...
Probability
1. Find the probability of each outcome when a biased die is rolled if rolling a 4 is twice as likely to appear as each of the other five numbers on the dice. If we roll this dice twice, what is the probability that the sum of the two numbers appear is 7.
Homework Answers
Solution:
Let 2p be the probability that dice outcome is 4 and so any other number will be the output with probability p. Since sum of all the outcome is 1.
So, p+p+p+p+p+2p=1
=> p = 1/7
When dice is roll 2 times, sum will be 7 when outcomes is either of these pairs (1,6),(6,1),(5,2),(2,5),(3,4),(4,3).
Probability of (1,6)= probability of (6,1)=probability of (5,2)= probability of (2,5) = p*p =p2 = 1/49
Probability of (4,3) = probability of (3,4) = 2p*p = 2/49
So total probability of sum to be 7 = 4/49 + 2* 2/49 = 8/49
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