Probability
A speaks the truth 2 out of 3 times and B speaks the truth 4 out of 5 times. Both agreed to the assertion that from a bag containing 6 balls i.e, red, blue, yellow, white, purple and orange, a red coloured ball has been taken out. If the probability of the statement being true can be expressed as p/q where p and q are natural co prime numbers, find the value of p+q.
The answer is 81.
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1 solution
P(red taken out & reported | red reported)
= { (1/6)[(2/3)(1/1)][(4/5)(1/1)] } / { (1/6)[(2/3)(1/1)][(4/5)(1/1)] + (5/6)[(1/3)(1/5)][(1/5)(1/5)] }
= { 8/90 } / { 8/90 + 5/2250 }
= 40 / 41
Answer = 40 + 41 = 81