The probability that a student passes subject a, b or c is 98%. the probability that he or she passes a is 41%, b is 59%. the probability that he or she passes a and c is 25% and b and c is 20%. the probability that he or she passes all the 3 subjects is 14%. what is the probability that he or she passes subject c?
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Using De Morgan's Laws,
P(a+b+c) = P(a)+P(b)+P(c)-P(a x b)-P(b x c)-P(a x c)+P(a x b x c)
P(a+b+c) = 98% or 0.98
P(a) = 41% or 0.41
P(b) = 59% or 0.59
P(c) = ?
P(a x b) is assumed to be= 0
P(a x c) = 25% = 0.25
P(b x c) = 20% = 0.20
P(a x b x c) = 14% = 0.14
Putting the values we get
0.98 = 0.41+0.59+ P(c) - 0.25 - 0.20 + 0 + 0.14
0.98 = 1.14 - 0.45 + P(c)
0.98 = 0.69 + P(c)
P(c) = 0.98-0.69
= 0.29.
P(a+b+c) = P(a)+P(b)+P(c)-P(a x b)-P(b x c)-P(a x c)+P(a x b x c)
P(a+b+c) = 98% or 0.98
P(a) = 41% or 0.41
P(b) = 59% or 0.59
P(c) = ?
P(a x b) is assumed to be= 0
P(a x c) = 25% = 0.25
P(b x c) = 20% = 0.20
P(a x b x c) = 14% = 0.14
Putting the values we get
0.98 = 0.41+0.59+ P(c) - 0.25 - 0.20 + 0 + 0.14
0.98 = 1.14 - 0.45 + P(c)
0.98 = 0.69 + P(c)
P(c) = 0.98-0.69
= 0.29.
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