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umka21 [38]
3 years ago
15

Suppose we have an unfair coin that its head is twice as likely to occur as its tail. a)If the coin is flipped 3 times, what is

the probability of getting exactly 1 head? Give your answer to four decimal places b)If the coin is flipped 5 times, what is the probability of getting exactly 2 tails? Give your answer to four decimal places c)If the coin is flipped 4 times, what is the probability of getting at least 3 tails? Give your answer to four decimal places
Mathematics
1 answer:
Alenkinab [10]3 years ago
8 0

Answer: a) 0.2222, b) 0.3292, c) 0.1111

Step-by-step explanation:

Since we have given that

Let the probability of getting head be p.

Since,  its head is twice as likely to occur as its tail.

p+\dfrac{p}{2}=1\\\\\dfrac{3p}{2}=1\\\\p=\dfrac{2}{3}

a)If the coin is flipped 3 times, what is the probability of getting exactly 1 head?

So, here, n  = 3

p=\dfrac{2}{3}

q=\dfrac{1}{3}

Now,

P(X=1)=^3C_1(\dfrac{2}{3})^1(\dfrac{1}{3})^2=0.2222

b)If the coin is flipped 5 times, what is the probability of getting exactly 2 tails?

2 tails means 3 heads.

So, it becomes,

P(X=3)=^5C_3(\dfrac{2}{3})^3(\dfrac{1}{3})^2=0.3292

c)If the coin is flipped 4 times, what is the probability of getting at least 3 tails?

P(X\leq 1)=\sum _{x=0}^1^4C_x(\dfrac{2}{3}^x(\dfrac{1}{3})^{4-x}=0.1111

Hence, a) 0.2222, b) 0.3292, c) 0.1111

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