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One coin in a collection of 5 is rigged to have a probability of showing heads equal to 0.2. The rest are fair (probability 0.5). A coin is chosen at random from the lot and tossed 3 times. It turns up heads 3 times in a row. What is the probability that it is the rigged coin given that it showed heads in 3 out of 3 tosses?

Respuesta :

Answer:

The probability that it is the rigged coin given that it showed heads in 3 out of 3 tosses is 0.0016.

Step-by-step explanation:

The probability of the chosen coin being rigged is [tex]\frac{1}{5}[/tex].

It is also given that, the outcome is a head all the 3 times.

The probability that all the outcomes will be head is [tex]0.2 \times0.2\times0.2 = 0.008[/tex].

According to the question, the probability is [tex]\frac{1}{5} \times0.008 = 0.0016[/tex].