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Sloan [31]
3 years ago
12

Can someone help me with this question?

Mathematics
1 answer:
belka [17]3 years ago
5 0

Answer:

The required probability is 0.0155.

Step-by-step explanation:

We are given that the one-year survival rate for pancreatic cancer is 20%.

Of 12 people diagnosed with pancreatic cancer at one hospital, 6 survived one year.

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 of trials (samples) taken = 12 people

            r = number of success = 6 survived

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

                  one-year survival rate for pancreatic cancer, i.e; p = 20%

Let X = <u><em>Number of people survived one year</em></u>

So, X ~ Binom(n = 12 , p = 0.20)

Now, the probability that 6 survived one year is given by = P(X = 6)

              P(X = 6)  =  \binom{12}{6} \times 0.20^{6} \times (1-0.20)^{12-6}

                             =  924 \times 0.20^{6} \times 0.80^{6}

                             =  <u>0.0155</u>

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