Fruit Flles An experiment with fruit flies involves one parent with notmal wings and ooe parent with vestigial wings. When these parents have an ofring, there is a 3/4 probabulty that the ofring has normal wings and a 1/4/4 probability of vestigial wings. If the parents give birth to five ofring. What is the probability that at least one of the ofring has vestigial wings? If researchers need at least one ofring with vestigial wings, can they be quite conte dent of getting one?

Fruit Flles An experiment with fruit flies involves one parent with notmal wings and ooe parent with vestigial wings. When these parents have an ofring, there is a 3/4 probabulty that the ofring has normal wings and a 1/4/4 probability of vestigial wings. If the parents give birth to five ofring. What is the probability that at least one of the ofring has vestigial wings? If researchers need at least one ofring with vestigial wings, can they be quite conte dent of getting one?

Question
Probability
asked 2021-03-02
Fruit Flles An experiment with fruit flies involves one parent with notmal wings and ooe parent with vestigial wings. When these parents have an of \(\displaystyle\frac{{3}}{{4}}\) probabulty that the of \(\displaystyle\frac{{1}}{{4}}/{4}\) probability of vestigial wings. If the parents give birth to five of

Answers (1)

2021-03-03

The probability that all of the of \(\displaystyle{\left(\frac{{3}}{{4}}\right)}^{{5}}=\frac{{{3}^{{5}}}}{{{4}^{{5}}}}\)
since they are independent.
The event that at least one of them has vestigial wings is a complementary event to the event that all have normal wings, so
P(at least one has vestigial wings)=1-{(all have normal wings)=\(\displaystyle{1}-\frac{{{3}^{{5}}}}{{{4}^{{5}}}}=\frac{{781}}{{1024}}\sim{76.27}\%\)
So, there is a good chance that there will be at least one of them with vestigial wings.
\(\displaystyle\frac{{781}}{{1024}}\sim{76.27}\%\)

0

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