In a box carrying one dozen of oranges, one third have become bad. If 3 oranges are taken out from the box at random, what is the probability that at least one oranges out of the three oranges picked up is good?

Q: In a box carrying one dozen of oranges, one third have become bad. If 3 oranges are taken out from the box at random, what is the probability that at least one oranges out of the three oranges picked up is good?

n(S) = 12C3 = (12 x 11 x 10) / (3 x 2) = 2 x 11 x 10 = 220 No. of selecting of 3 oranges out of the total 12 orange = 4C3 = 4 ∴ n(E) = No. of desired selection of oranges = 220 - 4 = 216 ∴ P(E) = n(E) / n(S) = 216 / 220 = 54/55

1/55
54/55
45/55
3/55

Correct Answer: 54/55

Explanation:

n(S) = ¹²C₃ = (12 x 11 x 10) / (3 x 2) = 2 x 11 x 10 = 220
No. of selecting of 3 oranges out of the total 12 orange = ⁴C₃ = 4
∴ n(E) = No. of desired selection of oranges = 220 - 4 = 216
∴ P(E) = n(E) / n(S) = 216 / 220 = 54/55

← Previous Question Next Question→

More Questions from Probability

What is the probability that a leap year selected randomly will have 53 Mondays?
What is the probability that a leap year selected randomly will have 53 Mondays?
If the probability for A fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails is?
A fair coin is tossed 100 times . The probability of getting tails an odd number of times is?
A natural number is selected at random from the set x = { x : 1 ≤ x ≤ 100 }. The probability that the number satisfies the inequality x 2 - 13x ≤ 30 is?
The probability that 9 students pass in Mathematics, Physics and Chemistry are m, p and c respectively, of these subject the students has a 75% chance of passing in at least one subject 50% chance of passing in at least two subject and 40% chance of passing in exactly two. Which of the following relation are true?
If the integer m and n are chosen at random between 1 and 100, then the probability that a number of the from 7 m + 7 n is divisible by 5 equals?
If n integer taken at random are multiplied together then the probability that the last digit of the product is 2, 4, 6, 8 is?
Two dice and two coins are tossed. The probability that both the coins show head and the sum of the numbers found on the two dice is a prime number is?
A speaks truth in 60% of the cases and B in 80% of the cases. In what percentage of cases are they likely to contradict each other, narrating the same incident?

Discussion & Comments

No comments yet. Be the first to comment!

Join Discussion