6% of male are color-blind. Find the probability that the first color-blind will be found among the first 5 men tested.

UkusakazaL 2021-08-10 Answered
6% of male are color-blind. Suggest a male groub is randomly selected and tested, find the probability that the first color-blind will be found among the first 5 men tested.

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Expert Answer

Rivka Thorpe
Answered 2021-08-04 Author has 3559 answers

Geometric probability formula:
\(\displaystyle{P}{\left({X}={k}\right)}={q}^{{{k}-{1}}}{p}={\left({1}-{p}\right)}^{{{k}-{1}}}{p}\)
p=6%
k=1, 2, 3, 4, 5:
\(\displaystyle{P}{\left({X}={1}\right)}={\left({1}-{0.06}\right)}^{{{1}-{1}}}{\left({0.06}\right)}={0.94}^{{0}}{\left({0.06}\right)}={0.06}\)
\(\displaystyle{P}{\left({X}={1}\right)}={\left({1}-{0.06}\right)}^{{{2}-{1}}}{\left({0.06}\right)}={0.94}^{{1}}{\left({0.06}\right)}={0.0564}\)
\(\displaystyle{P}{\left({X}={1}\right)}={\left({1}-{0.06}\right)}^{{{3}-{1}}}{\left({0.06}\right)}={0.94}^{{2}}{\left({0.06}\right)}={0.053016}\)
\(\displaystyle{P}{\left({X}={1}\right)}={\left({1}-{0.06}\right)}^{{{4}-{1}}}{\left({0.06}\right)}={0.94}^{{3}}{\left({0.06}\right)}={0.049835}\)
\(\displaystyle{P}{\left({X}={1}\right)}={\left({1}-{0.06}\right)}^{{{5}-{1}}}{\left({0.06}\right)}={0.94}^{{4}}{\left({0.06}\right)}={0.0468449}\)
\(P(A\ or\ B)=P(A)+P(B)\). So,
\(\displaystyle{P}{\left({X}\le{5}\right)}={P}{\left({X}={1}\right)}+{P}{\left({X}={2}\right)}+{P}{\left({X}={3}\right)}+{P}{\left({X}={4}\right)}+{P}{\left({X}={5}\right)}\)
=0.06+0.0564+0.053016+0.049835
=0.2660959
=26.60959%

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