Question

There are 3 true coins and 1 false coin with 'head' on both sides. A coin is chosen at random and tossed 4 times. If 'head' occurs all the 4 times, then probability that the false coin has been chosen and used is

15/19
14/19
131/19
16/19

Answer 1

131 / 19 ........................

Answer 2

If 'head' occurs all the 4 times, then probability that the false coin has been chosen and used is option (4): 16/19.

Step-by-step explanation:

It is given that there are 3 true coins and 1 false coin with head on both sides.

So,

The probability that the coin is true coin, P(T) = $\frac{3}{4}$

The probability that the coin is false coin, P(F) = ¼

Let’s assume the event of getting all heads in four tosses be “A”.  

Then,

The probability getting heads on all 4 tosses of a true coin,  

P(A/T) = ½ * ½ * ½ * ½  = $\frac{1}{16}$

And,

The probability of getting head on all 4 tosses of a false coin is,

P(A/F) = 1

Thus,  

The probability that the false coin has been chosen and used is,

= P(F/A)

= $\frac{P(F) * P(A/F)}{[{P(F) * P(A/F)} + { P(T) * P(A/T)}]}$

= $\frac{(1/4) * 1}{[(1/4) * 1] + [(3/4) * (1/16)]}}$

= $\frac{1}{1 + \frac{3}{16}}$

= $\frac{1}{\frac{19}{16}}$

= $\frac{16}{19}$

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Also View:

If a coin is thrown three times what is the probability of getting heads all three times?

https://brainly.in/question/9306565

3 coins are tossed at the same time,what is the probability of getting

a) one head

b)2 heads

c)no heads

d)at least one head

e)at most two tails

https://brainly.in/question/11316423