Activity (Probability) You are planning to create a casino night for charity. For the casino, you have set up a card game in which a player picks a card from a standard deck of 52 cards. The player wins if these two events occur together: E1, in which the card drawn is a black card, and E2, in which the card drawn is a numbered card, 2 through 10.

1) What is the probability of getting a black card and a numbered card? Calculate the probabilities P(E1) and P(E2) as fractions.

2) Find the number of sample outcomes that are common to the two events.

3) Write the probability of the intersection of the events, P(E1 ∩ E2).

4) Find the probability that the card drawn is a numbered card or a black card.

5) Find the probability that the card drawn is not a numbered card.

6) What is the sample space of a trial in which you draw one card twice from a set of 4 kings: spade, club, diamond, and heart. The card is replaced in the set before the second draw.

7) By completing the activities in questions 2 and 3, you have found that different events have different probabilities. For the charitable casino night you are planning, would it be better to assign more points to the events with high probabilities of payout? Why or why not?

8) Considering what you have learned from this activity, how does the number of plays affect the success of your casino night?