1.an eight biased die is rolled three times. die is baised in such way that the probability of getting any number is proportional to square of that number. what is the probability of getting first three even numbers consecutively?
Answers
Given : an eight biased die is rolled three times.
die is biased in such way that the probability of getting any number is proportional to square of that number.
To Find : what is the probability of getting first three even numbers consecutively
Solution:
8 side die is given
probability of 1 = k
probability of 2 = 2²k = 4k
probability of 3 = 9k
probability of 4 =16k
probability of 5 = 25k
probability of 6 = 36k
probability of 7 = 49k
probability of 8 = 64k
Total k + 4k + 9k + 16k + 25k + 36k + 49k + 64k = 204k
204k = 1
=> k = 1/204
first three even numbers in 3 throws
Probability of getting 2 = 4k
Probability of getting 4 = 16k
Probability of getting 6 = 36k
as these 3 can be in any sequence
Probability = 3! * 4k * 16K * 36
= 6 * 4 * 16 * 36 * k³
= 96 * 144 / (204)³
= 8 / 17³
= 8/4913
= 0.001628
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Step-by-step explanation:
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