A friend of yours claims to have a psychic gift. You are skeptical. To test his
ID: 3326317 • Letter: A
Question
A friend of yours claims to have a psychic gift. You are skeptical. To test his gift, you take the ace of hearrts, ace of spades, ace of diamonds, and ace of clubs from a deck of cards and show her the 4 cards. You turn the cards face down and shuffle them. You randomly choose 1 of the 4 cards removed from the deck and ask your friend (without seeing the card) to tell you what it is. You replace the card and repeat the experiment 4 times. If your friend is really not a psychic (and is guessing), what is the probabiloity that he guesses at least one of the four cards correctly? Round to 4 decimals.
Explanation / Answer
number of trials = 4
P[ correct guessing ] = 1/4 = 0.25
X is a random variable denoting the number of times she guesses correctly.
P [ X>=1] = 1 - P [ X =0] = 1 - 4C0 (0.25)0 (0.75)4 = 1 - 0.316406 = 0.683594
rounding off 0.683494 we get 0.6835