Question Video: Determining the Probability of Intersection of Two Independent Events | Nagwa Question Video: Determining the Probability of Intersection of Two Independent Events | Nagwa

# Question Video: Determining the Probability of Intersection of Two Independent Events Mathematics • Third Year of Secondary School

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A bag contains 15 blue balls and 10 red balls. A ball is chosen at random and the color is recorded. The ball is then replaced and another ball is chosen at random from the bag. What is the probability that the first ball is blue and the second ball is red?

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### Video Transcript

A bag contains 15 blue balls and 10 red balls. A ball is chosen at random, and the color is recorded. The ball is then replaced, and another ball is chosen at random from the bag. What is the probability that the first ball is blue and the second ball is red?

The probability of any event occurring can be written as a fraction, the number of successful outcomes over the number of possible outcomes. The bag contains 15 blue balls. Therefore, the probability of selecting a blue ball is 15 out of 25, as there are 25 balls altogether. This fraction can be simplified by dividing the numerator and denominator by five. 15 divided by five is three, and 25 divided by five is five. Therefore, the probability that the first ball is blue is three out of five or three-fifths.

As the ball is replaced, there will still be 25 balls in the bag when the second ball is selected. We need to calculate the probability that the second ball is red. This will be 10 out of 25, as 10 of the balls are red and there are 25 in total. Once again, this can be simplified so that the probability the second ball is red is two out of five or two-fifths.

We need to calculate the probability the first ball is blue and the second ball is red. The AND rule in probability states we need to multiply. We need to multiply three-fifths by two-fifths. When multiplying two fractions, we multiply the numerators and then multiply the denominators separately. This gives us an answer of six over 25 or six twenty-fifths. The probability that the first ball is blue and the second ball is red is six out of 25.

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