Probability of Satisfactory Tools in Packed Boxes: Solving for P

[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?

 

[tiny-tim]

Hi rclakmal!

(try using the X² tag just above the Reply box )

[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.

 

[rclakmal]

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;
then answer is
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 ...!