Question

an urn contains 4 red and 3 blue balls. One ball is selected randomly.If red ball is selected you win $3, otherwise you lose $ 5. Define a random variable giving these payoffs and give its probability distribution.

Answer 1

A random variable X is defined to represent the outcome of winning $3 for a red ball and losing $5 for a blue ball, with a probability distribution of P(X = $3) = 4/7 and P(X = -$5) = 3/7.

Step-by-step explanation:

The student is asking about creating a random variable for the scenario of drawing balls from an urn. In this scenario, the random variable (let's call it X) will represent the monetary outcome of the game, where X can take on two possible values, $3 for drawing a red ball and -$5 for drawing a blue ball.

The probability distribution of X is as follows:

• P(X = $3) = Probability of drawing a red ball = Number of red balls / Total number of balls = 4/7
• P(X = -$5) = Probability of drawing a blue ball = Number of blue balls / Total number of balls = 3/7

Therefore, the probability distribution for the random variable X is:

P(X = $3) = 4/7

P(X = -$5) = 3/7