yapafw

2021-11-17

In a university examination, which was indeed very tough, $50\mathrm{%}$ at jeast failed in "Statistics",$75\mathrm{%}$ at least in Topology, $82\mathrm{%}$ at least in "Functional Analysis" and $96\mathrm{%}$ at least in "Applied Mathematics". How many at least failed in all the four? (Ans.$3\mathrm{%}$)

Warajected53

Given
P(failed in Statistics) $=0.50$
P(failed in Topology) $=0.75$
P(failed in Functional Analysis) $=0.82$
P(failed in Applied Maths) $=0.96$
To find:
How many failed in at least all four
A, B, C and D are said to be independent when : $P\left(A\cap B\cap C\cap D\right)=P\left(B\right)×P\left(C\right)×P\left(D\right)$
The probability of failing in at least all four is given by:
P(failed in Statistics $\cap$ failed in Topology $\cap$ failed in Functional Analysis $\cap$ failed in Applied Maths)
= P(failed in Statistics) $×$ P(failed in Topo log y) X P(failed in Functional Analysis) $×$ P(failed in Applied Maths)

$=0.50×0.75×0.82×0.96$
=0. 2952
$\stackrel{\sim }{=}0.3$
Therefore, $3\mathrm{%}$ of them at least failed in all the four.

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