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?

Step-by-step explanation:

The probability of the chosen coin being rigged is .

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

The probability that all the outcomes will be head is .

According to the question, the probability is .

1st integer x

2nd integer x+1

3rd integer x+2

4th integer x+3

x+x+1 +x+2+x+3 =74

combine like terms

4x+6 = 74

subtract 6 from each side

4x = 68

x = 17

the integers are 17,18,19,20