Q. 245.0( 4 Votes )

X is taking up subjects – Mathematics, Physics and Chemistry in the examination. His probabilities of getting grade A in these subjects are 0.2, 0.3 and 0.5 respectively. Find the probability that he gets

i. Grade A in all subjects

ii. Grade A in no subjects

iii. Grade A in two subjects

Answer :

Given:


P(MA) = P(getting A in mathematics)


P(MA) = 0.2


P(MN) = P(not getting A in mathematics)


P(MN) = 1-0.2


P(MN) = 0.8


P(PA) = P(getting A in physics)


P(PA) = 0.3


P(PN) = P(not getting A in physics)


P(PN) = 1-0.7


P(PN) = 0.3


P(CA) = P(getting A in Chemistry)


P(CA) = 0.5


P(CN) = P(not getting A in chemistry)


P(CN) = 1-0.5


P(CN) = 0.5


We need to find the probability that:


i. X gets A in all subjects


ii. X gets A in no subjects


iii. X gets A in two subjects


P(Xall) = P(getting A in all subjects)


Since getting A in different subjects is an independent event, their probabilities multiply each other


P(Xall) = (P(MA)P(PA)P(CA))


P(Xall) = 0.2×0.3×0.5


P(Xall) = 0.03


P(Xnone) = P(getting A in no subjects)


Since getting A in different subjects is an independent event, their probabilities multiply each other


P(Xnone) = (P(MN)P(PN)P(CN))


P(Xnone) = 0.8×0.7×0.5


P(Xnone) = 0.28


P(Xtwo) = P(getting A in any two subjects)


Since getting A in different subjects is an independent event, their probabilities multiply each other


P(Xtwo) = (P(MA)P(PA)P(CN)) + (P(MA)P(PN)P(CA)) + (P(MN)P(PA)P(CA))


P(Xtwo) = (0.2×0.3×0.5) + (0.2×0.7×0.5) + (0.8×0.3×0.5)


P(Xtwo) = 0.03 + 0.07 + 0.12


P(Xtwo) = 0.22


The required probabilities are 0.03, 0.28, 0.22.


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