Two students h and k appeared in an examination. The probability that h will qualify the exam is 0.05 and that the probability that k will qualify the examination is 0.21. The probibality that both will qualify the examination is 0.03 find the probibality that .(a)both h and k will not qualify the examination(b)only h will qualify the examination(c)only k will qualify the examination(d)only one of them will qualify the examination
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
a) (1-.05)(1-.21) = ?
b) .05(1-.21) = ?
c) Follow same process.
d) This is saying that either h or k will qualify. Either-or probabilities are found by adding the individual probabilities.
Add answers from b and c.
To find the probability for each event, we will use basic probability rules.
Given information:
- Probability of h qualifying the exam (P(h)) = 0.05
- Probability of k qualifying the exam (P(k)) = 0.21
- Probability of both h and k qualifying the exam (P(h and k)) = 0.03
(a) To find the probability that both h and k will not qualify the examination:
P(h' and k') = 1 - P(h and k)
P(h' and k') = 1 - 0.03
P(h' and k') = 0.97
So, the probability that both h and k will not qualify the examination is 0.97.
(b) To find the probability that only h will qualify the examination:
P(h and k') = P(h) - P(h and k)
P(h and k') = 0.05 - 0.03
P(h and k') = 0.02
So, the probability that only h will qualify the examination is 0.02.
(c) To find the probability that only k will qualify the examination:
P(h' and k) = P(k) - P(h and k)
P(h' and k) = 0.21 - 0.03
P(h' and k) = 0.18
So, the probability that only k will qualify the examination is 0.18.
(d) To find the probability that only one of them will qualify the examination:
P(h and k') + P(h' and k)
= P(h) - P(h and k) + P(k) - P(h and k)
= 0.05 - 0.03 + 0.21 - 0.03
= 0.2
So, the probability that only one of them will qualify the examination is 0.2.