Advertisements
Advertisements
Question
Two thirds of students in a class are boys and rest girls. It is known that the probability of a girl getting a first grade is 0.85 and that of boys is 0.70. Find the probability that a student chosen at random will get first grade marks.
Advertisements
Solution
Let G be the event of choosing a boy and G be the event of choosing a girl.
Given P(B) = `2/3`
P(G) = `1/3`
Let B1 be the event of a boy getting first grade
P(B1) = 0.70
Let G1 be the event of a girl getting first grade
P(G1) = 0.85
Probability of a student getting a first grade = Probability of a boy getting first grade or Probability
of a Girl getting first grade
= P(B) × P(B1) + P(G) × P(G1)
= `2/3 xx 0.70 + 1/3 x 0.85`
= `(1.4 + 0.85)/3`
= `2.25/3`
= 0.75
APPEARS IN
RELATED QUESTIONS
Evaluate P(A ∪ B), if 2P(A) = P(B) = `5/13` and P(A | B) = `2/5`
Given that the two numbers appearing on throwing the two dice are different. Find the probability of the event ‘the sum of numbers on the dice is 4’.
If a leap year is selected at random, what is the chance that it will contain 53 Tuesdays?
If A and B are events such as that P(A) = `1/2`, P(B) = `1/3` and P(A ∩ B) = `1/4`, then find
1) P(A / B)
2) P(B / A)
In an examination, 30% of students have failed in subject I, 20% of the students have failed in subject II and 10% have failed in both subject I and subject II. A student is selected at random, what is the probability that the student has failed in at least one subject?
A bag contains 10 white balls and 15 black balls. Two balls are drawn in succession without replacement. What is the probability that, first is white and second is black?
An urn contains 4 black, 5 white, and 6 red balls. Two balls are drawn one after the other without replacement, What is the probability that at least one ball is black?
From a pack of well-shuffled cards, two cards are drawn at random. Find the probability that both the cards are diamonds when first card drawn is kept aside
A problem in Mathematics is given to three students whose chances of solving it are `1/3, 1/4` and `1/5`. What is the probability that exactly one of them will solve it?
Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if P(B/A) = 0.5
In a multiple-choice question, there are three options out of which only one is correct. A person is guessing the answer at random. If there are 7 such questions, then the probability that he will get exactly 4 correct answers is ______
If P(A) = `3/10`, P(B) = `2/5` and P(A ∪ B) = `3/5`, then P(B|A) + P(A|B) equals ______.
If P(A) = `2/5`, P(B) = `3/10` and P(A ∩ B) = `1/5`, then P(A|B).P(B'|A') is equal to ______.
If P(A) = `1/2`, P(B) = 0, then `P(A/B)` is
A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is ______.
Let A and B be two non-null events such that A ⊂ B. Then, which of the following statements is always correct?
For a biased dice, the probability for the different faces to turn up are
| Face | 1 | 2 | 3 | 4 | 5 | 6 |
| P | 0.10 | 0.32 | 0.21 | 0.15 | 0.05 | 0.17 |
The dice is tossed and it is told that either the face 1 or face 2 has shown up, then the probability that it is face 1, is ______.
If for two events A and B, P(A – B) = `1/5` and P(A) = `3/5`, then `P(B/A)` is equal to ______.
A Problem in Mathematics is given to the three students A, B and C. Their chances of solving the problem are `1/2, 1/3` and `1/4` respectively. Find the probability that exactly two students will solve the problem.
