# Solve the following: A die is loaded in such a way that the probability of the face with j dots turning up is proportional to j for j = 1, 2, .......6. What is the probability, in one roll of the die - Mathematics and Statistics

Sum

Solve the following:

A die is loaded in such a way that the probability of the face with j dots turning up is proportional to j for j = 1, 2, .......6. What is the probability, in one roll of the die, that an odd number of dots will turn up?

#### Solution

Let P(j) be the probability that j dots tum up, 1 ≤ j ≤ 6

∴ P(j) = jk, where k is the constant of proportionality

∴ sum_("j" = 1)^6 "P"("j") = 1

∴ k + 2k + 3k + 4k + 5k + 6k = 1

∴ 21k = 1

∴ k = 1/21

∴ the required probability = P(1) + P(3) + P(5)

= k + 3k + 5k = 9k

= 9/21   ...[because "k" = 1/21]

= 3/7.

Concept: Concept of Probability
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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 9 Probability
Miscellaneous Exercise 9 | Q II. (8) | Page 214