Respuesta :
Answer:
0.31104
Step-by-step explanation:
Given that according to the Sydney Morning Herald, 40% of bicycles stolen in Holland are recovered.
If X represents the number of bicyles stolen in Sydney, X is binomial
because each cycle to be stolen is independent of the other.
Also there are two outcomes
n = 6, p = 0.40
Required probability = the probability that, in a sample of 6 randomly selected cases of bicycles stolen in Holland, exactly 2 out of 6 bikes are recovered
==P(X=2)
=[tex]6C2 (0.4)^2 (0.6)^4\\= 15(0.16)(0.6)^4\\=0.31104[/tex]
Answer:
Probability that exactly 2 out of 6 bikes are recovered is 0.31.
Step-by-step explanation:
We are given that according to the Sydney Morning Herald, 40% of bicycles stolen in Holland are recovered.
Also, there is a sample of 6 randomly selected cases of bicycles stolen in Holland.
The above situation can be represented through Binomial distribution;
[tex]P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....[/tex]
where, n = number of trials (samples) taken = 6 cases of bicycles
r = number of success = exactly 2
p = probability of success which in our question is % of bicycles
stolen in Holland that are being recovered, i.e; 40%
LET X = Number of bikes recovered
So, it means X ~ [tex]Binom(n=6, p=0.40)[/tex]
Now, Probability that exactly 2 out of 6 bikes are recovered is given by = P(X = 2)
P(X = 2) = [tex]\binom{6}{2}0.40^{2} (1-0.40)^{6-2}[/tex]
= [tex]15 \times 0.40^{2} \times 0.60^{4}[/tex]
= 0.31
Therefore, Probability that, in a sample of 6 randomly selected cases of bicycles stolen in Holland, exactly 2 out of 6 bikes are recovered is 0.31.
