Find the indicated probability Round to three decimal places

Find the indicated probability. Round to three decimal places. 11) A machine has 12 identical components which function independently. The probability that a component will (ail is 0.2. The machine will stop working if more than three components fail. Find the probability that the machine will be working.

Solution

The random variable X=the machine will stop working follows a binomial distribution with n=12, p=0.2.

The m/c stops working if more than 3 components fail.

Thus, the prob. That the m/c will be working is:

1-P(X<=3)

=1-P(X=0)-P(X=1)-P(X=2)-P(X=3)

=1-12C0*0.2^0*0.8^12-12C1*0.2^1*0.8^11-12C2*0.2^2*0.8^10-12C3*0.2^3*0.8^9

=1-0.068-0.206-0.283-0.236

=0.207