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?

1 Answer
Feb 18, 2018

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