Lance threw a die six times. His median score was 3.5. His first five throws were 1.5, 3, 5, 1. What was his sixth throw?
Answers
Answer:
what is diversity means that you have any other example
Answer:
Let E
1
be the event that the outcome on the die is 5 or 6 and E
2
be the event that the outcome on the die is 1,2,3 or 4.
∴P(E
1
)=
6
2
=
3
1
and P(E
2
)=
6
4
=
3
2
Let A be the event of getting exactly one head.
P(A∣E
1
)= Probability of getting exactly one head by tossing the coin three times if she gets 5 or 6 =
8
3
P(A∣E
2
)= Probability of getting exactly one head in a single throw of coin if she gets 1,2,3 or 4 =
2
1
The probability that the girl threw 1,2,3 or 4 with the die, if she obtained exactly one head, is given by P(E
2
∣A).
By using Bayes' theorem, we obtain
P(E
2
∣A)=
P(E
1
)⋅P(A∣E
1
)+P(E
2
)⋅P(A∣E
2
)
P(E
2
)⋅P(A∣E
2
)
=
3
1
⋅
8
3
+
3
2
⋅
2
1
3
2
⋅
2
1
=
3
1
(
8
3
+1)
3
1
=
8
11
1
=
11
8
=0.72