Question

According to the Sydney Morning Herald, 40% of bicycles stolen in Holland are recovered. (In contrast, only 2% of bikes stolen in New York City are recovered.) Find the probability that, in a sample of 6 randomly selected cases of bicycles stolen in Holland, exactly 2 out of 6 bikes are recovered. Find the nearest answer.

Answer 1

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;

$P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....$

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 ~ $Binom(n=6, p=0.40)$

Now, Probability that exactly 2 out of 6 bikes are recovered is given by = P(X = 2)

   P(X = 2) = $\binom{6}{2}0.40^{2} (1-0.40)^{6-2}$

                 = $15 \times 0.40^{2} \times 0.60^{4}$

                 = 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.

Answer 2

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)

=$6C2 (0.4)^2 (0.6)^4\\= 15(0.16)(0.6)^4\\=0.31104$