Question

A box contains three cards. On one card there is a question mark (Q), on another card there is a rectangle (R), and on the third card there is a pear (P). Two cards are to be selected at random with replacement. Complete parts (a) through (e) below List the sample space. Choose the correct answer below
QQ QR, QP, RQ, RR, RP. PQ, PR, PP OB.
QR QP, Ra, RP, PQ, PR OC.
QQ, QR, QP, PQ, PR, PP
O D. QR, RP, PQ
c) Determine the probability that two rectangles are selected The probability is(Simplity your answer.)
d) Determine the probability that a card containing a rectangle and then a card containing a question mark are selected The probability is(Simplity your answer.)
e) Determine the probability that at most one card containing a question mark is selected The probability is _____

Answer 1

Answer:

(a) QQ, QR, QP, RQ, RR, RP. PQ, PR, PP

(c) $\frac{1}{9}$

(d) $\frac{2}{9}$

(e) $\frac{4}{9}$

Step-By-Step Explanation:

(a)Sample Space

Since there is replacement, for the second pick, we can still pick the previous card.

Therefore, the Sample Space = QQ, QR, QP, RQ, RR, RP. PQ, PR, PP

(c) Probability that two rectangles are selected  

$P(RR)= \frac{1}{3} X \frac{1}{3} \\= \frac{1}{9}$

(d) Probability that a card containing a rectangle and then a card containing a question mark are selected.

$P(RQ) or P(QR)= (\frac{1}{3} X \frac{1}{3})+(\frac{1}{3} X \frac{1}{3}) \\= \frac{1}{9}+\frac{1}{9}\\=\frac{2}{9}$

(e) Probability that at most one card containing a question mark is selected.

$P(RQ) or P(QR) or P(QP) Or P(PQ)= (\frac{1}{3} X \frac{1}{3})+(\frac{1}{3} X \frac{1}{3})+(\frac{1}{3} X \frac{1}{3}) +(\frac{1}{3} X \frac{1}{3}) \\= \frac{1}{9}+\frac{1}{9}+\frac{1}{9}+\frac{1}{9}\\=\frac{4}{9}$