The probability of getting heads from throwing a fair coin is 1/2. The fair coin

Question

The probability of getting heads from throwing a fair coin is 1/2. The fair coin is tossed 4 times. What is the probability that exactly 3 heads occur? The fair coin is tossed 4 times. What is the probability that exactly 3 heads occur given that the first outcome was a head? The fair coin is tossed 4 times. What is the probability that exactly 3 heads occur given that the first outcome was a tail? The fair coin is tossed 4 times. What is the probability that exactly 3 heads occur given that the first two outcomes were heads? The fair coin is tossed 4 times. What is the probability that exactly 3 heads occur given that there is at least 1 head? A coin is rigged so that the probability of heads is 5/7 The rigged coin is tossed 4 times. What is the probability that exactly 3 heads occur? The rigged coin is tossed 4 times. What is the probability that exactly 3 heads occur given that the first outcome was a head? The rigged coin is tossed 4 times. What is the probability that exactly 3 heads occur given that the first outcome was a tail? The rigged coin is tossed 4 times. What is the probability that exactly 3 heads occur given that the first two outcomes were heads? The rigged coin is tossed 4 times. What is the probability that exactly 3 heads occur given that there is at least 1 head?

Explanation / Answer

SOlving the first question, Please repost the others individually

n=4,p=1/2,q=1/2

a)P(3 heads) = 4C3 * (1/2)^3*(1/2) = 4/16=0.25

b)P( 3 heads/ 1st is heads) = 3C2*(1/2)^2*(1/2)=3/8

c)P( 3 heads/1st is tails) = 3C3*(1/2)^3=1/8

d)P( 3 heads/1st two are heads) = P(1 head in two trials)2C1*(1/2)^2=1/2

e)P( exactly 3 /at least one head) = 4C3*(1/2)^4/[1-1/2^4'=4/16 /[15/16]=4/15

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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