Answer:
0.139
Step-by-step explanation:
We are given that
Total number of cards=52
n=18
We have to find the probability of drawing at least 7 spades
Total number of spaded in deck of 52 cards=13
Probability of getting spade=[tex]p=\frac{13}{52}=\frac{1}{4}[/tex]
Probability,[tex]P(E)=\frac{favorable\;cases}{total\;number\;of\;cases}[/tex]
Probability of getting no spade=[tex]q=1-p=1-\frac{1}{4}=\frac{3}{4}[/tex]
By binomial theorem of probability
[tex]P(X=x)=\binom{n}r}p^rq^{n-r}[/tex]
P(x[tex]\geq 7)=1-P(x\leq 6)[/tex]
The probability of drawing at least 7 spades=[tex]1-\sum_{r=0}^{6}\binom{18}{r}(\frac{3}{4})^{18-r}(\frac{1}{4})^r[/tex]
The probability of drawing at least 7 spades=0.139
