If a coin is tossed one time then the probability of a head is 1/2. If we toss a coin 18 times, then what is the probability of getting a head?
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B.L. Srivastava, M.Sc.Ph.D. Mathematics, Chhatrapati Shahu Ji Maharaj University
Answered Sep 24, 2018
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Tossing of a coin is a random process and turning of a head or a tail on it is an event and it follows Binomial distribution. That is Prob. of r success is given by ;
P(X = r ) = C(n,r) (p^r)(q^(n-r)) . Where p is prob.of success and q Prob. of failure and C(n,r) = n!/r!(n-r)! .Clearly here in this case, we have in a toss of a coin;
Prob. of turning of a head (success) = p =1/2 = 0.5 ,
Prob. of turning of a tail (failure) =q = (1 -1/2 ) = 1/2 = 0.5
Case 1. Prob. of getting exactly no head in the 18 tosses of the coin,
P(X = 0) = C(18,0)·(0.5)^0{(0.5)^18}
= (0.5)^18 = 0.0000038147.
ThereforeThereforeprob. of getting at least 1 head
= P( X > = 1 ) = 1 - 0.0000038147
=0.999996=0.999996(which is almost = 1) ..
Case 2. Prob. of getting exactly 1 head in 18 tosses of the coin ;
P(X = 1) = C(18,1)(0.5)^1{0.5}^17
== 18 ××(0.5)^18=0.000068664
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probability of getting Head = 1 - 1/ 2¹⁸ = 0.999996 ( almost 1)
Step-by-step explanation:
If a coin is tossed one time then the probability of a head is 1/2.
If we toss a coin 18 times, then what is the probability of getting a head?
P (H) = 1/2
P (T) = 1 - 1/2 = 1/2
we toss a coin 18 times he probability of getting a head
= 1 - Probability of getting 0 Heads
= 1 - ¹⁸C₀(1/2)⁰(1/2)¹⁸
= 1 - 1 / 2¹⁸
= 0.999996
Almost 1
Prob. of getting exactly 1 head in 18 tosses of the coin
= ¹⁸C₁(1/2)¹(1/2)¹⁷
= 0.000068
alomost 0
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Answer:
Divide 50 by 18 easy.
Step-by-step explanation:
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