34% of working mothers do not have enough money to cover their health insurance deductibles. you randomly…

Answer:

x	P(x)
0	0.106
1	0.294
2	0.329
3	0.198
4	0.069
5	0.013
6	0.001

Explanation:

Step1: Recall binomial - probability formula

The binomial - probability formula is $P(x)=C(n,x)\times p^{x}\times(1 - p)^{n - x}$, where $C(n,x)=\frac{n!}{x!(n - x)!}$, $n$ is the number of trials, $x$ is the number of successes, and $p$ is the probability of success on a single trial. Here, $n = 6$ and $p=0.34$, so $1 - p = 0.66$.

Step2: Calculate $P(0)$

$C(6,0)=\frac{6!}{0!(6 - 0)!}=1$, $P(0)=C(6,0)\times(0.34)^{0}\times(0.66)^{6}=1\times1\times0.0828524576\approx0.106$.

Step3: Calculate $P(1)$

$C(6,1)=\frac{6!}{1!(6 - 1)!}=\frac{6!}{1!5!}=6$, $P(1)=C(6,1)\times(0.34)^{1}\times(0.66)^{5}=6\times0.34\times0.1255340267\approx0.294$.

Step4: Calculate $P(2)$

$C(6,2)=\frac{6!}{2!(6 - 2)!}=\frac{6\times5}{2\times1}=15$, $P(2)=C(6,2)\times(0.34)^{2}\times(0.66)^{4}=15\times0.1156\times0.189= 0.329$.

Step5: Calculate $P(3)$

$C(6,3)=\frac{6!}{3!(6 - 3)!}=20$, $P(3)=C(6,3)\times(0.34)^{3}\times(0.66)^{3}=20\times0.039304\times0.287496\approx0.198$.

Step6: Calculate $P(4)$

$C(6,4)=\frac{6!}{4!(6 - 4)!}=15$, $P(4)=C(6,4)\times(0.34)^{4}\times(0.66)^{2}=15\times0.01336336\times0.4356\approx0.069$.

Step7: Calculate $P(5)$

$C(6,5)=\frac{6!}{5!(6 - 5)!}=6$, $P(5)=C(6,5)\times(0.34)^{5}\times(0.66)^{1}=6\times0.0045435424\times0.66\approx0.013$.

Step8: Calculate $P(6)$

$C(6,6)=\frac{6!}{6!(6 - 6)!}=1$, $P(6)=C(6,6)\times(0.34)^{6}\times(0.66)^{0}=1\times0.00154480449\times1\approx0.001$.