0.216
To find the probability that three randomly selected farmers are all in debt, given the probability that a single farmer is in debt is 0.60, we can use the concept of independent probability. Here, for three independent events (each farmer being in debt), the combined probability is the product of the individual probabilities.
- Given that the probability of a single farmer being in debt is \(0.60\).
- Assume that each farmer's debt status is independent of the others.
- The probability of all three farmers being in debt is: \(P(\text{all in debt}) = 0.60 \times 0.60 \times 0.60\).
- Calculating the product, we have: \(0.60 \times 0.60 = 0.36\).
- Now, multiply \(0.36\) by \(0.60\): \(0.36 \times 0.60 = 0.216\).
Thus, the probability that all three randomly selected farmers are in debt is 0.216.
| Option | Probability |
|---|---|
| 0.216 | Correct |
| 0.064 | Incorrect (Computed as \(0.40 \times 0.60 \times 0.60 = 0.144\)) |
| 0.000216 | Incorrect (Miscalculation likely at \(0.60^3\)) |
| 0.512 | Incorrect (Misunderstanding of probability of failure \(0.40^3\)) |
Hence, the correct option is 0.216.
Tip: When probabilities are independent, the combined probability of multiple events is the product of individual probabilities.
Similar Questions
- What is the probability that getting a total of the numbers on the dice is 6 ?
- What is the probability that getting a total of the numbers on the dice is at least 23 ?
- The probability that a family owns a laptop is 0.68; that it also owns a desktop is 0.56. If the probability that it owns both is 0.48, then what is the probability that a randomly selected family owns a laptop or a desktop?
Important Questions from Probability
Two dice are thrown simultaneously and the sum of the numbers appearing on them is noted. What is the probability that the sum is 12?
If a box contains 3 white cushions, 4 red cushions and 5 blue cushions, what is the probability of selecting a white or blue cushion?
A. 2/3
B. 3/4
C. 1/4
D. 1/9Statements followed by some conclusions are given below.
Statements:
1. A bag has 2 white, 3 black, 4 red and 6 green balls.
2. 1 ball selected at random from the bag.
Conclusions:
I. The probability that a black ball is selected is 1/5
II. The probability that a red ball is selected is 6/15
Find which of the conclusions logically follows from the given statement
A. Only conclusion I follows.
B. Only conclusion II follows.
C. Both I and II follow.
D. Neither I nor II follows.
In a shooting test, the probabilities of hitting the target are 1/2 for A, 2/3 for B and 3/4 for C. If they fire at the same target, what is the probability that only one of them hits the target?
A bag contains balls numbered from 1 to 42. One ball is drawn at random from these balls. The probability that its number is a multiple of 7 or 8 is:
