Abby writes a test in maths and in science.The probability that she passes maths is 0.6.
The probability that she passes science is 0.7.The two tests are independent of each other.Calculate the probability that Abby:
a)Passes science and fails maths
b)Fails both tests
To calculate the probabilities, we will use the multiplication rule for independent events.
a) To calculate the probability that Abby passes science and fails maths, we multiply the probability of passing science (0.7) by the probability of failing maths (1 - 0.6 = 0.4) since the events are independent.
P(passes science and fails maths) = P(passes science) * P(fails maths)
= 0.7 * 0.4
= 0.28
Therefore, the probability that Abby passes science and fails maths is 0.28.
b) To calculate the probability of failing both tests, we multiply the probability of failing maths (1 - 0.6 = 0.4) by the probability of failing science (1 - 0.7 = 0.3) since the events are independent.
P(fails both tests) = P(fails maths) * P(fails science)
= 0.4 * 0.3
= 0.12
Therefore, the probability that Abby fails both tests is 0.12.