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A six faced dice is tossed. If a prime number occurs sumeet wins that many number of rupees. But, if a non–prime number occurs he loses that many number of rupees. Determine whether the game is favourable or unfavorable to the player.
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Solution | |
Let "x" indicate the amount that sumeet wins [Since you are required to find the expected earning of sumeet, the variable would represent sumeets earnings] The amount earned by sumeet would be
Non- Prime Numbers from 1 to 6 ⇒ {1, 4, 6} ⇒ The values carried by the variable ("x") would be either − 1, + 2, + 3, − 4, + 5 or − 6
"X" represents the random variable and P(X = x) represents the probability that the value within the range of the random variable is a specified value of "x" In the experiment of tossing a dice, there are six possible elementary events, the events of the die showing up either ONE, TWO, THREE, FOUR, FIVE or SIX all of which are mutually exclusive, equally likely and exhaustive. Therefore the probability of occurance of each elementary event is 1/6 Probabilty that the dice would show up
Probability for the amount earned by sumeet to be
The probabilty distribution of "x" would be
Calculations for Mean and Variance
Expectation of the persons gain
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Credit : Vijayalakshmi Desu |