Respuesta :
Answer:
P(2 low,4 average, 2 high) = 0.0356
Step-by-step explanation:
We are given the following information in the question:
Total number of batteries = 40
Number of batteries with average lifetime = 30
Number of batteries with low lifetime = 5
Number of batteries with high lifetime = 5
Total number of possibilities of selecting 8 batteries from 40 batteries =
[tex]^{40}C_8 = \displaystyle\frac{40!}{8!\times 32!} = 76904685[/tex]
Total number of possibilities of selecting 2 low lifetime batteries from 5 batteries =
[tex]^{5}C_2 = \displaystyle\frac{5!}{2!\times 3!} = 10[/tex]
Total number of possibilities of selecting 4 average lifetime batteries from 30 batteries =
[tex]^{30}C_4 = \displaystyle\frac{30!}{4!\times 26!} = 27405[/tex]
Total number of possibilities of selecting 2 high lifetime batteries from 5 batteries =
[tex]^{5}C_2 = \displaystyle\frac{5!}{2!\times 3!} = 10[/tex]
Formula:
[tex]\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}[/tex]
[tex]=\displaystyle\frac{10\times 27405\times 10}{76904685} = 0.0356[/tex]
The probability of exactly 2 low, 4 average, and 2 high lifetimes batteries is 0.0356 or 3.56%.
What is probability?
Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
A box contains 40 batteries, 5 of which have low lifetimes, 30 of which have average lifetimes, and 5 of which have high lifetimes.
A consumer requires 8 batteries to run an appliance and randomly selects them all from the box.
The probability that among the 8 batteries fitted into the consumer’s appliance, there are exactly 2 low, 4 average, and 2 high lifetimes batteries will be
[tex]\rm P = \dfrac{^5C_2*^{30}C_4*^5C_2}{ ^{40}C_{8} } \\\\\\ P = \dfrac{10*27405*10}{76904685}\\\\\\P = 0.0356\\\\P = 3.56 \%[/tex]
More about the probability link is given below.
https://brainly.com/question/795909
