(a) What Is the probability that when tossing 20 independent coins whose probabi

Question

(a) What Is the probability that when tossing 20 independent coins whose probability of coming up heads is 3/4, exactly 12 of the coins will turn up heads?
(b) Toss a fair coin 8 times, what is the probability that the fourth head will occur on the sixth toss? (a) What Is the probability that when tossing 20 independent coins whose probability of coming up heads is 3/4, exactly 12 of the coins will turn up heads?
(b) Toss a fair coin 8 times, what is the probability that the fourth head will occur on the sixth toss?
(b) Toss a fair coin 8 times, what is the probability that the fourth head will occur on the sixth toss?

Explanation / Answer

BIONOMIAL DISTRIBUTION
pmf of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
where
k = number of successes in trials   
n = is the number of independent trials   
p = probability of success on each trial
I.
mean = np
where
n = total number of repetitions experiment is excueted
p = success probability
mean = 20 * 0.75
= 15
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 20 * 0.75 * 0.25
= 3.75
III.
standard deviation = sqrt( variance ) = sqrt(3.75)
=1.936492
a.
P( X = 12 ) = ( 20 12 ) * ( 0.75^12) * ( 1 - 0.75 )^8
= 0.060887
b.
will check for tossing a 5 coin will get exactly 3 heads and then add the probability
of next coin toss head, this satisfy tossing of 6 coins 4th heads occurs on 6th turn.
P( X = 3 ) = ( 5 3 ) * ( 0.75^3) * ( 1 - 0.75 )^2
= 0.263672

P( next coin toss is also a head) = 0.263672 * 0.75 = 0.197754

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

---

---

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