# Probability of Satisfactory Tools in Packed Boxes: Solving for P

• rclakmal
In summary, the problem is asking to find the value of P that satisfies the equation 3P^4 - 8P^3 + 6P^2 - 0.95 = 0, given that the probability of a box containing at least 2 satisfactory tools is 0.95. This can be solved using the binomial distribution formula, where N = 4 and r = 2, 3, 4. After solving, the answer is P = 0.5.

#### rclakmal

[tools producing company packed them in boxes of 4.probability that a tool is satisfactory P.If the probability that a box contains at least 2 satisfactory tools is to be 0.95.show that 3P^(4) -8P^(3)+6P^(2)-0.95=0
should be satisfy by P. How to approach this answer?

Hi rclakmal!

(try using the X2 tag just above the Reply box )
rclakmal said:
[tools producing company packed them in boxes of 4.probability that a tool is satisfactory P.If the probability that a box contains at least 2 satisfactory tools is to be 0.95.show that 3P^(4) -8P^(3)+6P^(2)-0.95=0
should be satisfy by P. How to approach this answer?

Hint: probability that a tool is unsatisfactory is 1 - P.

And probability that a box contains at least 2 satisfactory tools is 1 minus probability that it contains exactly 0 minus probability that it contains exactly 1.

these days I am fighting with the time ..exam papers and theories are going simultaneously. after publishing this question i studied about binomial distribution .then i got to know that this problem should be solve by that .

by using binomial theorem i was able to solve it as getting N=4 and r=2,3,4;
0.95=SIGMA (r goes 2 to 4)= 4Cr*p^r*(1-p)
then i got the answer ...thanks TINY TIM ...ur a great helping hand to me ...

hoping ur help in the future also ...!

## What is probability?

Probability is the measure of the likelihood of an event occurring. It is represented as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

## What is the difference between theoretical and experimental probability?

Theoretical probability is based on the possible outcomes of an event, while experimental probability is based on the actual outcomes of an event after conducting an experiment or observation.

## How do you calculate probability?

Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This can be represented as a fraction, decimal, or percentage.

## What is the difference between independent and dependent events?

Independent events are events where the outcome of one event does not affect the outcome of another event. Dependent events are events where the outcome of one event does affect the outcome of another event.

## What is the difference between mutually exclusive and overlapping events?

Mutually exclusive events are events that cannot occur at the same time. Overlapping events are events that can occur together or separately.