An unfair coin has the property that when flipped 4 times, it has the same non-zero probability of turning up 2 heads and 2 tails in any order) as 3 heads and 1 tail (in any order). Let p be the probability of getting a head in any one flip, find the value of 60p.
Please give the right answer with explanation.
Answers
Given : An unfair coin has the property that when flipped 4 times, it has the same non-zero probability of turning up 2 heads and 2 tails (in any order) as 3 heads and 1 tail (in any order).
p be the probability of getting a head in any one fiip,
To Find : Value of 60p
Solution:
Coin flipped 4 times
probability of head in any one flip = p
probability of tail in any one flip = 1 - p
2 heads and 2 tails
= ⁴C₂(p)²(1 - p)² = 6p²(1 - p)²
3 heads and 1 tail
= ⁴C₃(p)³(1 - p) = 4p³(1- p)
Equate both
6p²(1 - p)² = 4p³(1- p)
=> 3(1 - p) = 2p
=> 3 - 3p = 2p
=> 3 = 5p
=> p = 3/5
=> 60p = 60 * 3/5 = 36
value of 60p is 36
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