Question

A random experiment consists in choosing and integer between 1 and 4, inclusive. The probability of choosing a number is inversely proportional to the square root of the number. For example, the probability of choosing 4 is half the probability of choosing 1.

Using the rules of probability, determine the probability of the elementary events.

Find the probability that the chosen number is odd.

Find the probability that the chosen number is even, given that it is less than 4.

Answer 1

P(X = c) = k / sqrt(c)

P(X = 1) + P(X = 2) + P(X =3) + P(X =4) = 1

k/sqrt(1) + k/sqrt(2) + k / sqrt(3) + k/sqrt(4) = 1

hence

k (1 + 1/sqrt(2) + 1/ sqrt(3) + 1/sqrt(4) ) = 1

k *2.784457 = 1

k = 1 /2.784457 = 0.359136449

Find the probability that the chosen number is odd.

= P(X = 1) + P(X = 3)

= k + k/sqrt(3) = 0.35913644 * ( 1 + 1/sqrt(3)) = 0.56648

P(X = even |X < 4) = P(X = 2 or 4 and X < 3)/P(X < 3)

= P(X = 2) /P(X <3)

= 1/sqrt(2) / (1 + 1/sqrt(2) + 1/sqrt(3))

= 0.309529

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answered by: anonymous