help me with this problem please

Question

The alphabet game costs $.25 to play. Before the game, 26 slips of paper with a different letter of the alphabet on it are put into a bag. A player draws one slip from the bag. If the player draws a vowel (A, E, I, O, or U), he or she wins $1. If a player plays the alphabet game 2 times in a row, replacing the slip of paper after each turn, what is the probability that they win twice? Write as a fraction.

I need the thrid one

Answer 1

Hi Emme:

Let's do this one!

The probability of winning on the first draw = Pr {drawing a vowel}

= # vowels available / # letters available

= 5/26

After the first draw, the slip is returned => the situation is unchanged for the second draw

So, probability of winning on the second draw = 5/26

Now, these 2 events (draw #1 and draw #2) are independent events, => they do not influence each other

Therefore, the probability of winning twice = (5/26) x 5/26 = 25/ 676 = 3.7%