Answered

At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

A certain insecticide kills 60% of all insects in laboratory experiments. A sample of 7 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 4 insects will survive? Round your answer to four decimal places.

Sagot :

reinhard10158

Step-by-step explanation:

the probability of 1 tested insect is killed is 60% or 0.6.

the probability that it is not killed is then 1-0.6 = 0.4.

when we test 7 insects and exactly 4 survive is the event that

3 insects are killed, 4 insects survive.

the probability for one such case is

0.6×0.6×0.6 × 0.4×0.4×0.4×0.4

how many such cases do we have ?

as many as ways we can select 4 insects out of the given 7.

these are 7 over 4 combinations :

7! / (4! × (7-4)!) = 7! / (4! × 3!) = 7×6×5/(3×2) = 7×5 = 35

so, the probability that exactly 4 out of 7 tested insects survive is

35 × 0.6³ × 0.4⁴ = 0.193536 ≈ 0.1935

Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.