3 learners are taking a maths test, the probability that Maria passes is 0,9; Katlego 0,7; Mpho is 0,6.
1. What is the probability that:
- all three pass?
Maria and Mpho pass but Katlego fails?
- All three fail?
- at least one of them passes?
prob(all three pass) = (0.9)(0.7)(0.6) = ....
prob(Maria and Mpho pass but Katlego fails) = 0.9(0.7)(.4) = ...
prob(all fail) = .....
prob(at least one will pass) = 1 - prob(all fail)
To find the probability of multiple independent events, you multiply the individual probabilities of each event. Let's calculate the probabilities for each of the given scenarios:
1. All three pass:
To find the probability that all three learners pass, you need to multiply the probabilities of each individual passing.
P(Maria passes) = 0.9
P(Katlego passes) = 0.7
P(Mpho passes) = 0.6
P(all three pass) = P(Maria passes) * P(Katlego passes) * P(Mpho passes)
= 0.9 * 0.7 * 0.6
= 0.378
Therefore, the probability that all three learners pass is 0.378 or 37.8%.
2. Maria and Mpho pass, but Katlego fails:
To find the probability that Maria and Mpho pass while Katlego fails, you multiply the probabilities of Maria and Mpho passing and subtract the probability of Katlego passing.
P(Maria passes) = 0.9
P(Katlego passes) = 0.7
P(Mpho passes) = 0.6
P(Maria and Mpho pass but Katlego fails) = P(Maria passes) * P(Mpho passes) * (1 - P(Katlego passes))
= 0.9 * 0.6 * (1 - 0.7)
= 0.9 * 0.6 * 0.3
= 0.162
Therefore, the probability that Maria and Mpho pass but Katlego fails is 0.162 or 16.2%.
3. All three fail:
To find the probability that all three learners fail, you need to subtract the probability of all three passing from 1.
P(all three fail) = 1 - P(all three pass)
= 1 - 0.378
= 0.622
Therefore, the probability that all three learners fail is 0.622 or 62.2%.
4. At least one of them passes:
To find the probability that at least one of the learners passes, you can calculate the probability of the complement event (none of them passing) and subtract it from 1.
P(at least one passes) = 1 - P(all three fail)
= 1 - 0.622
= 0.378
Therefore, the probability that at least one of the learners passes is 0.378 or 37.8%.
I hope this helps! Let me know if you have any other questions.