Question

Pennsylvania has a lottery entitled "Big 4". To win, a player must correctly match 4 digits, in order, from a daily lottery in which four digits are selected. Digits are chosen from four separate bins, each containing 10 balls numbered 0-9. The only way to win is to match all 4 digits. If the payoff for a $100 bet is $10000, what is the expected value of winning? Create the probability model for this situation. Based on the model, is it worth playing? Feel free to use StatCrunch to write the model and find the expected value, then include your screen shot as a picture.

Answer 1

The probability of winning the bet that is getting all the 4 digits matched is computed here as:
= (1/10)*(1/10)*(1/10)*(1/10)
= 1/10000

Therefore the expected value of the bet here is computed as:
= - Cost of Bet + Expected Payoff

= -100 + 10000 / 10000

= -100 + 1

= -99

Therefore the expected value of the winning here is given as -99 (note that it includes the fee to take part in the bet)