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johnnyaby69
31.03.2020 •
Mathematics
The probability that a certain make of car will need repairs in the first six months is 0.4. A dealer sells seven such cars. What is the probability that at least one of them will require repairs in the first six months?
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Ответ:
0.972
Step-by-step explanation:
This problem can be solved binomialy with n = 7
The probability that the car will need repair ; p(need repair) = 0.4
The probability that the car will not need repair ; p(no repair) = 1 - 0.4 = 0.6
Probability at least 1 will need repair = 1 - Probability none will need repair
Probability at least 1 will need repair = 1 - p(no repair)
=![1-(0.6)^{7} = 0.972](/tpl/images/0572/5040/006e1.png)
Ответ:
Probability that at least one of them will require repairs in the first six months is 0.972.
Step-by-step explanation:
We are given that the probability that a certain make of car will need repairs in the first six months is 0.4. A dealer sells seven such cars.
The above situation can be represented through Binomial distribution;
where, n = number of trials (samples) taken = 7 cars
r = number of success = at least one
p = probability of success which in our question is probability that a
make of car will need repairs in the first six months, i.e; 0.40
LET X = Number of cars that require repairs in the first six months
So, it means X ~![Binom(n=7, p=0.40)](/tpl/images/0572/5040/737a8.png)
Now, Probability that at least one of them will require repairs in the first six months is given by = P(X
1)
P(X
1) = 1 - P(X = 0)
=![1- \binom{7}{0}\times 0.40^{0} \times (1-0.40)^{7-0}](/tpl/images/0572/5040/ad587.png)
=![1-( 1 \times 1 \times 0.60^{7})](/tpl/images/0572/5040/7581e.png)
=
= 0.972
Therefore, Probability that at least one of them will require repairs in the first six months is 0.972.
Ответ:
i need help on math
Step-by-step explanation: