Micha is playing a game with five cards numbered 1 through 5. He will place the cards in a bag and draw one card at random three
times, replacing the card each time. To win a prize, he must draw the number 5 all three times. What is the probability he will draw the number 5 all three times?
Each experiment is exactly the same: "Drawing the card with the number 5, out of a bag with five cards".
in a random selection all the cards have exactly the same probability of being drawn, so the probability of drawing the 5, is equal to the quotient between the number of cards with the 5 (only one) and the total number of cards in the bag (5) then the probability is:
p = 1/5.
And we want this event to happen 3 consecutive times, then the total probability is equal to the product of the probabilities for each event:
Area of the square: A s = s². Area of the circle: A c = ( 1/2 s )² π = 1/4 s² · 3.14 = 0.785 s² Area inside the square but outside the circle: s² - 0.785 s² = 0.215 s² The ratio: 0.215 s² : s² = 0.215 : 1 = 215 : 1000 = 43 : 200 .
