Probability of getting " heads" with 5 biased coins.

label Mathematics
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Yasmin has 5 coins. One of these coins is biased with P(heads) = 0.6. The other 4 coins are fair. She tosses all 5 coins once and records the number of heads, X

 Question: Show that P(X = 1) = 0.1375.

How will you answer this?

May 17th, 2015

You can ask back if you have any doubt. I am here.

May 17th, 2015

P(X = 1) = (0.6 × 0.54) + (4 × 0.4 × 0.5× 0.53)  

= 0.0375 + 0.1 = 0.1375 


This is the answer they gave, it seems very different to your answer.

May 17th, 2015

Both answers are same, kindly check that

(4 × 0.4 × 0.5 × 0.5^3)  = (4 × 0.4 × 0.5^4) 

I have just added powers directly. You know rules of exponents.

May 17th, 2015

it is not 0.53 and 0.54. it is 0.5 raised to the power 3 and 0.5 raised to the power 4.

May 17th, 2015

are you getting it?

May 17th, 2015

I followed by taking 0.5^4 common and other solution is following by without taking common. It is just like taking two different roots to same destination.

May 17th, 2015

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