To define a probability model for the experiment of picking a card from a selection of cards numbered 510 and 15, we first need to consider the random variable \( X \) that represents the outcome of this experiment. Since the cards are numbered, the possible outcomes (values of \( X \)) are just the numbers on the cards.
The possible values of \( X \) are:
- \( 510 \)
- \( 15 \)
In ascending order, the values of \( X \) would be \( 15, 510 \).
Next, if we assume that each card is equally likely to be picked, we can say that the probability \( F(x) \) of picking each card is as follows:
- For \( X = 15 \): \( P(X = 15) = \frac{1}{2} \)
- For \( X = 510 \): \( P(X = 510) = \frac{1}{2} \)
Thus, the cumulative probability function \( F(x) \) would be defined as:
- \( F(x) = 0 \) for \( x < 15 \)
- \( F(x) = \frac{1}{2} \) for \( 15 \leq x < 510 \)
- \( F(x) = 1 \) for \( x \geq 510 \)
In conclusion, we can represent the probability model as follows:
- \( F(x) = P(X) \)
- where \( x = 15, 510 \)
So you would fill in the blanks like this:
- \( F(x) = \frac{1}{2} \) for \( x = 15, 510 \)