Suppose that you flip a coin 14 times. What is

Wanda Kane

Wanda Kane

Answered question

2021-12-21

Suppose that you flip a coin 14 times. What is the probability that you achieve at least 4 tails?

Answer & Explanation

Travis Hicks

Travis Hicks

Beginner2021-12-22Added 29 answers

Step 1
Given Information:
Suppose that you flip a coin 14 times.
To find the probability that you achieve at least 4 tails:
Let X be a random variable which denotes the number of tails and X follows Binomial distribution with number of trials n=14 and probability of success p=0.5
(Since, P(T)=12=0.5)
Probability mass function of Binomial variable X is given by the formula:
P(X=x)=nCxpx(1p)nx;x=0,1,2..14
Step 2
Required probability is obtained as follows:
P(X4)=1P(X<4)
=1[P(X=0)+P(X=1)+P(X=2)+P(X=3)]
=1[{14}C0(0.5)0(10.5)140+14C1(0.5)1(10.5)141+14C2(0.5)2(10.5)142+14C3(0.5)3(10.5)143]
=1[14!0!(140)!×1×0.00006103515625+14!1!(141)!×0.5×0.0001220703125+14!2!(142)!×0.25×0.000244140625+14!3!(143)!×0.125×0.00048828125]
=1[1×0.00006103515625+14×0.00006103515625+91×0.00006103515625+364×0.00006103515625]
=1[0.00006103515625+0.0008544921875+0.005554199219+0.02221679688]
=10.02868652344
=0.9713134766
0.9713
Thus, the probability that you achieve at least 4 tails is 0.9713
peterpan7117i

peterpan7117i

Beginner2021-12-23Added 39 answers

Step 1
Binomial distribution:
P(x)=nCx pxqnx
P (tails), p=0.5
q=10.5=0.5
Number of trials, n=14
Pat least 4 tails}=1P(less than 4 tails)
=1[P(0)+P(1)+P(2)+P(3)]
=1[0.514+14×0.5×0.513+14C2×0.52×0.512+14C3×0.53×0.511]
=0.9713
nick1337

nick1337

Expert2021-12-28Added 777 answers

Probability of flipping either a head or a tail
=12
Probability of flipping 6 tails in a row
(12)6
Probability of flipping at least 1 head
=1(12)6=6364

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