Question

3. Consider the following:

a. A game was advertised as having a probability of 0.4 of winning. You know that the game involved five cards with a different digit on each card. Describe a possible game involving the
cards that would have a probability of 0.4 of winning.
b. A second game involving the same five cards was advertised as having a winning probability of 0.05. Describe a possible game that would have a probability of 0.05 or close to 0.05
of winning.

Answer 1

a.) Digits on the 5 cards are 1,2,3,4,5. You pick one card. You win if you pick a card having an even number.

b) Digits on the 5 cards are 1,2,3,4,5. You pick two cards. You win if you pick fist the card having number 5 and then the card having number 4.

Explanation:

a) The probability of picking an even number is:

picking a card with even numbers (picking 2 or 4) / all cards (1,2,3,4,5)

• 
  `(2)/(5) =0.4`

b) Probability of picking the card having 5 first

• 
  `(1)/(5)`

Then the probability of picking the card having number 4 from the remaining 4 cards:

• 
  `(1)/(4)`

Combined probability, that is picking first number 5 and then number 4 is

• 
  `(1)/(5) *(1)/(4) =(1)/(20) =0.05`