In a form 1A class there are 25 boys and 20 girls.in a form 1B there are 20boys and 15girls.A learner is choosen at random from each class.find the probability that
(a):both learners are boys
(b):the choosen learners are of different sexes????
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
a. 25/45 * 20/25 = ?
b. 25/45 * 15/25 = ?
or 20/45 * 20/25 = ?
Either-or probabilities are found by adding the individual probabilities.
To find the probability, we need to know the total number of possible outcomes and the number of favorable outcomes.
Let's find the probability for each case:
(a) Both learners are boys:
Total number of possible outcomes = Total number of learners in form 1A * Total number of learners in form 1B = (25 boys + 20 girls) * (20 boys + 15 girls) = 45 * 35 = 1575
Favorable outcomes = Number of ways to choose boys from form 1A * Number of ways to choose boys from form 1B = 25 * 20 = 500
Probability = Favorable outcomes / Total number of possible outcomes = 500 / 1575 ≈ 0.317
(b) The chosen learners are of different sexes:
Total number of possible outcomes = Total number of learners in form 1A * Total number of learners in form 1B = (25 boys + 20 girls) * (20 boys + 15 girls) = 45 * 35 = 1575
Favorable outcomes = Number of ways to choose a boy from form 1A and a girl from form 1B + Number of ways to choose a girl from form 1A and a boy from form 1B
= (25 * 15) + (20 * 20) = 375 + 400 = 775
Probability = Favorable outcomes / Total number of possible outcomes = 775 / 1575 ≈ 0.492
So, the probabilities are:
(a) Approximately 0.317
(b) Approximately 0.492
To find the probability of certain events, we need to first find the total number of possible outcomes and the number of favorable outcomes.
(a) Probability that both learners are boys:
In form 1A, there are 25 boys and 20 girls, so the total number of learners in form 1A is 25 + 20 = 45.
In form 1B, there are 20 boys and 15 girls, so the total number of learners in form 1B is 20 + 15 = 35.
To find the probability that both learners are boys, we need to multiply the probability of selecting a boy from each class.
P(Both learners are boys) = (Number of boys in form 1A / Total number of learners in form 1A) * (Number of boys in form 1B / Total number of learners in form 1B)
P(Both learners are boys) = (25/45) * (20/35)
(b) Probability that the chosen learners are of different sexes:
To find the probability that the learners are of different sexes, we need to find the probability of selecting a boy from one class and a girl from the other class. We can either select a boy from the first class and a girl from the second class or a girl from the first class and a boy from the second class.
P(The chosen learners are of different sexes) = (Probability of selecting a boy from form 1A and a girl from form 1B) + (Probability of selecting a girl from form 1A and a boy from form 1B)
P(The chosen learners are of different sexes) = ((Number of boys in form 1A / Total number of learners in form 1A) * (Number of girls in form 1B / Total number of learners in form 1B)) + ((Number of girls in form 1A / Total number of learners in form 1A) * (Number of boys in form 1B / Total number of learners in form 1B))
You can plug in the values to calculate the probabilities.