Respuesta :
Answer:1
_
25
Step-by-step explanation:
When you replace the ball after picking it, the probability remains the same for each trial. In this case, you have 3 red balls out of a total of
3
+
10
+
2
=
15
3+10+2=15 balls. The probability of picking a red ball on the first draw is:
�
(
Red on 1st draw
)
=
Number of red balls
Total number of balls
=
3
_
15
P(Red on 1st draw)=
Total number of balls
Number of red balls
=
15
3
After replacing the red ball, you still have 3 red balls out of 15. Therefore, the probability of picking a red ball on the second draw is the same:
�
(
Red on 2nd draw
)
=
3
15
P(Red on 2nd draw)=
15
3
Since the events are independent when replacement is allowed, you can multiply the probabilities:
�
(
Red on 1st and 2nd draws
)
=
�
(
Red on 1st draw
)
×
�
(
Red on 2nd draw
)
P(Red on 1st and 2nd draws)=P(Red on 1st draw)×P(Red on 2nd draw)
�
(
Red on 1st and 2nd draws
)
=
3
15
×
3
15
P(Red on 1st and 2nd draws)=
15
3
×
15
3
Simplify the fraction:
�
(
Red on 1st and 2nd draws
)
=
1
25
P(Red on 1st and 2nd draws)=
25
1
So, the probability of picking one red ball, replacing it, and then picking another red ball is
1
_
25
