# An urn contains five red balls and four white balls.  A sample of two balls is selected at random from the urn.  Find the probability that:a) only red balls are selectedb) at least one white ball is selected

Question

An urn contains five red balls and four white balls.  A sample of two balls is selected at random from the urn.  Find the probability that:

a) only red balls are selected

b) at least one white ball is selected

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Step 1

Concept of probability:

Probability deals with the likelihood of occurrence of a given event. The probability value lies between 0 and 1. An event with probability 1 is considered as certain event and an event with probability 0 is considered as an impossible event. The probability of 0.5 infers of having equal odds of occurring and not occurring of an event.

The general formula to obtain probability of an event A is,

P(A) = (number of favourable elements for event A)/(Total number of elements in the sample space).

The basic properties of probability are given below:

Step 2

Obtain the probability that at least one white ball is selected.

It is given that an urn contains of five red balls and four white balls.

The number of red balls is n(R) = 5.

The total number of balls or sample size is n(S) = 9.

Here, it is given that a sample of two balls is selected at random from a total of 9 balls.

The probability of drawing a red ball in the first selection is P(R1) = 5/9.

After drawing a red ball in the first selection, there will be 4 red balls and total of 8 balls remained in the urn.

The probability of drawing a red ball in the second selection is P(R2) = 4/8.

The requirement is both the selected balls has to be red in colour.

The probability that only red balls are selected is obtained as 0.2778 from the calculation given below:

Step 3

Obtain the probability that at least one white ball is selected.

The total number of balls or sample size is n(S) = 9.

Here, it is given that a sample of two balls is selected at random from a total of 9 balls.

The number of white balls is n(W) = 4.

The probability of drawing a white ball in the first selection is P(W) = 4/9.

The requirem...

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