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stiv31 [10]
3 years ago
15

The probability that an egg on a production line is cracked is 0.01. Two eggs are selected at random

Mathematics
1 answer:
ser-zykov [4K]3 years ago
6 0

Answer:

Probability that both eggs are cracked is 0.0001.

Step-by-step explanation:

We are given that the probability that an egg on a production line is cracked is 0.01.

Two eggs are selected at random  from the production line.

The above situation can be represented through binomial distribution;

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

where, n = number trials (samples) taken = 2 eggs

            r = number of success = both eggs are cracked

            p = probability of success which in our question is probability that

                 an egg on a production line is cracked, i.e; p = 0.01

<u><em>Let X = Number of eggs on a production line that are cracked</em></u>

So, X ~ Binom(n = 2, p = 0.01)

Now, Probability that both eggs are cracked is given by = P(X = 2)

                P(X = 2) =  \binom{2}{2} \times 0.01^{2} \times (1-0.01)^{2-2}

                              =   1\times 0.01^{2} \times 0.99^{0}

                              =  0.0001

<em>Therefore, probability that both eggs are cracked is </em><em>0.0001</em><em>.</em>

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