Question

In Bengal, 30% of the population has a certain blood type.What is the probability that exactly four out of a randomly selected group of 10 Bengalis will have that blood type?

Answer 1

`0.200`

Explanation:

The probability that four out of the ten people have that blood type is `0.3 * 0.3 * 0.3 * 0.3 = (0.3)^4`.

The probability that the other six do not have that blood type is `(1-0.3)^6 = (0.7)^6`.

We multiply these probabilities together, but since these outcomes can happen in any combination (for example, person 1, 2, 3, and 4 have the blood type, or perhaps 1, 2, 3, 5, etc.), we multiply by `color(white)I_10C_4`.

Thus, the probability is `(0.3)^4 * (0.7)^6 * color(white)I_10C_4 ~~ 0.200`.

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This is another way to do it:

Since having this specific blood type is a Bernoulli trial (there are only two outcomes, a success and a failure; the probability of success, `0.3`, is constant; and the trials are independent), we can use a Binomial model.

We will use `"binompdf"` because the "pdf", probability density function, allows us to find the probability of exactly four successes.

When using this function on your calculator, enter `10` for the number of trials, `0.3` for `p` (the probability of success), and `4` for the `X` value.

`"binompdf"(10, 0.3, 4) ~~ 0.200`