An urn of 10 balls contains 6 red ones. Two balls are taken at random. Then the probability that there is only

An urn of 10 balls contains 6 red ones. Two balls are taken at random. Then the probability that there is only one red among them is …

The event is such that among the balls taken out, only one red ball means that either the first time they took out a red ball, and the second time – a ball of a different color, or the first time they took out not a red ball, but the second time – a red one.
These are inconsistent events, so their probability is equal to the sum of the probabilities:
P = 6/10 4/9 + 4/10 6/9 = 24/90 + 24/90 = 48/90 = 8/15 ≈ 0.5333.
Answer: The probability that there is only one red ball among the balls taken out is 0.5333.