Question

Suppose that you randomly draw one card from a standard deck of 52 cards. After writing down which card was drawn, you replace the card, and draw another card. You repeat this process until you have drawn 18 cards in all. What is the probability of drawing at least 7 spades

Answer 1

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=$p=\frac{13}{52}=\frac{1}{4}$

Probability,$P(E)=\frac{favorable\;cases}{total\;number\;of\;cases}$

Probability  of getting no spade=$q=1-p=1-\frac{1}{4}=\frac{3}{4}$

By binomial theorem of probability

$P(X=x)=\binom{n}r}p^rq^{n-r}$

P(x$\geq 7)=1-P(x\leq 6)$

The probability of drawing at least 7 spades=$1-\sum_{r=0}^{6}\binom{18}{r}(\frac{3}{4})^{18-r}(\frac{1}{4})^r$

The probability of drawing at least 7 spades=0.139