A friend of yours claims to have the psychic gift. You are skeptical of her clai

Question

A friend of yours claims to have the psychic gift. You are skeptical of her claim. To test her gift. you take the ace of hearts, ace of spades, ace of diamonds, and ace of clubs from a deck of cards and show her the four cards. You turn the cards face down and shuffle them. You randomly choo one of the four 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 th experiment four times if your friend is really not a psychic (and is merely guessing at the cards), what is the probability that she guesses the first two cards correctly and guesses the last two cards incorrectly? Round your answer to four decimal places Answer 1 Point Keypad Tables

Explanation / Answer

Let E be the event of guessing the card from sample space S (hearts,spades,diamonds,clubs)
Every time favourable outcomes is 1 (one of spades,hearts,diamonds ,clubs)
Probability of guessing right = Favourable events / Total Sample Space => 1/4 => .25
Probability of guessing wrong =1-.25 => .75

a) P(first two correct) = 0.25^2 = 0.0625

b) P(last two incorrect) = 0.75^2 = 0.5625

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