Suppose you draw cards at random from an ordinary deck of 52 cards, with replace

Question

Suppose you draw cards at random from an ordinary deck of 52 cards, with replacement. (You return each card to the deck and shuffle thoroughly before drawing the next card.) You draw cards until you get a heart or until you have drawn 4 cards. Let X be the number of cards you draw. Answer the following questions to three places after the decimal. a) What is P(X-1)? Submit Ancwr Tries 0/2 b) What is P(X-2)? Submit Ancwr Tries 0/2 c) What is P(X-3)? Submit Answor Tries 0/2 d) What is P(X-4)? Submit Ancwer Tries 0/2

Explanation / Answer

The probability of getting a heart in each trial is 1/4 = 0.25.

Since replacement is allowed, the probability remains same.

Probability of not getting a heart in each trial = 1 - 0.25 = 0.75.

=> The probability that a heart turns up in the nth attempt

= 0.75n-1 0.25

except in the case where four cards are drawn where the draws stop and the probability there is simply 0.753

a) P(X = 1) = 0.250

b) P(X = 2) = 0.75 * 0.25 = 0.1875 = 0.188

c) P(X = 3) = 0.75 * 0.75 * 0.25 = 0.140625 = 0141

d) P(X = 4) = 0.75 * 0.75 * 0.75 = 0.421875 = 0.422

e) P(X < 3) = P(1) + P(2) = 0.250 + 0.188 = 0.438.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.