Advertisements
Advertisements
Question
Data on readership of a magazine indicates that the proportion of male readers over 30 years old is 0.30 and the proportion of male readers under 30 is 0.20. If the proportion of readers under 30 is 0.80. What is the probability that a randomly selected male subscriber is under 30?
Solution
Let E1 be the event of the subscriber is under 30 and E2 be the event of the subscriber is above 30.
Let B be the event of the subscriber is a male.
Given P(E1) = 0.80 and P(E2) = 1 − 0.8 = 0.2
and P`("B"/"E"_1)` = 20, P`("B"/"E"_2)` = 0.30
∴ `"P"("E"_1/"B") = ("P"("E"_1) xx "P"("B"/"E"_1))/("P"("E"_1) xx "P"("B"/"E"_1) + "P"("E"_2) xx "P"("B"/"E"_2))`
= `(0.80 xx 0.20)/(0.80 xx 0.20 + 0.20 xx 0.30)`
= `0.16/(0.16 + 0.06)`
= `0.16/0.22`
= `16/22`
∴ `"P"("E"_1/"B")` = 0.727
APPEARS IN
RELATED QUESTIONS
From a pack of 52 cards, two cards are drawn at random. Find the probability that one is a king and the other is a queen.
The events A and B are independent if
Let a sample space of an experiment be S = {E1, E2, ..., En}, then `sum_("i" = 1)^"n" "P"("E"_"i")` is equal to
The probability of obtaining an even prime number on each die, when a pair of dice is rolled is
Gun 1 and Gun 2 are shooting at the same target. Gun 1 shoots on the average nine shots during the same time Gun 2 shoots 10 shots. The precision of these two guns is not the same. On the average, out of 10 shots from Gun 2 seven hit the target. In the course of shooting the target has been hit by a bullet, but it is not known which Gunshot this bullet. Find the chance that the target was hit by Gun 2?
What is the chance that leap year should have fifty three Sundays?
An integer is chosen at random from the first 100 positive integers. What is the probability that the integer chosen is a prime or multiple of 8?
A cricket club has 16 members, of whom only 5 can bowl. What is the probability that in a team of 11 members at least 3 bowlers are selected?
The odds that the event A occurs is 5 to 7, find P(A)
Choose the correct alternative:
An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. The probability that the second ball drawn is red will be
