1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
tangare [24]
3 years ago
9

The Reds and the Cubs are playing 3 games. In each game the probability that the Reds win is 0.54. The probability of the Reds w

inning is not affected by who has won any previous games.
(a) What is the expected value for the number of games the Reds will win? (Give your answer correct to two decimal places.) _______

(b) What is the expected value for the number of games the Cubs will win? (Give your answer correct to two decimal places.) _______
Mathematics
1 answer:
shusha [124]3 years ago
8 0

Answer:

(a) 1.6197

(b) 1.3803

Step-by-step explanation:

(a) Let X denote the number of games the Reds win. If Reds win exactly one it means that in the other two games Reds lost i.e Cubs won. Now,  the probability of the Reds losing is determined by 1 -\text{probability of winning} = 1-0.54 = 0.46. So, if X wins exactly i times, then we should multiply the probabilities associated with

P(X=0) = \binom{3}{0} \times 0.46 \times 0.46 \times 0.46 = 0.0973

P(X=1) = \binom{3}{1} 0.54 \times 0.46 \times 0.46 = 0.3429

P(X=2) = \binom{3}{2} 0.54 \times 0.54 \times 0.46 = 0.4023

P(X=3) = \binom{3}{3} 0.54 \times 0.54 \times 0.54 = 0.1574

Now,

E(X) = \sum_{i=0}^{3} i \times P(X=i) = 1.6197

(b) Let Y denote the number of games won by Cubs. Then by the similar logic as above,

P(Y=3) = \binom{3}{0} 0.46 \times 0.46 \times 0.46 = 0.0973

P(Y=2) = \binom{3}{1} 0.54 \times 0.46 \times 0.46 = 0.3429

P(Y=1) = \binom{3}{2} 0.54 \times 0.54 \times 0.46 = 0.4023

P(Y=0) = \binom{3}{3} 0.54 \times 0.54 \times 0.54 = 0.1574

Now

E(Y) = \sum_{j=0}^{3} j \times P(Y=j) = 1.3803

You might be interested in
25m + 100 - 24m - 75 = 68.
Maksim231197 [3]

25m+100−24m−75=68

Step 1: Simplify both sides of the equation.

25m+100−24m−75=68

25m+100+−24m+−75=68

(25m+−24m)+(100+−75)=68(Combine Like Terms)

m+25=68

m+25=68

Step 2: Subtract 25 from both sides.

m+25−25=68−25

m=43

Answer:

m=43

8 0
3 years ago
Jason ran 7/8 of a mile in 12 minutes. How many miles can Jason run in 1 hour?
Scrat [10]
Its technically like 7/8 x 60 because 60 mins is an hour
4 0
3 years ago
Read 2 more answers
SOMEONE please just explain this to me I need to pass
Temka [501]

Answer:

4

Step-by-step explanation:

I think I'm not that sure

8 0
2 years ago
Read 2 more answers
If f(x)=3x² - 4 and g(x)=x+2, find (f - g)(x).​
nika2105 [10]

Answer:

D

Step-by-step explanation:

(f - g)(x)

= f(x) - g(x)

= 3x² - 4 - (x + 2) ← distribute parenthesis by - 1

= 3x² - 4 - x - 2 ← collect like terms

= 3x² - x - 6

3 0
2 years ago
Suppose radius CA is a 12 meters long. What is the diameter of the circle
Romashka [77]

Answer:

24m

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • Need help with a math question
    11·1 answer
  • Bobcat Park is a rectangular park with an area of 5 2/5 square miles.Its width is 1 11/25 miles.How long is the park?
    7·1 answer
  • Hello, I need help with this question (it has multiple parts. See attached.) PLEASE show ALL of your work, down to the bone! I o
    15·1 answer
  • Which of the following functions is graphed below
    14·1 answer
  • The endpoints of are A(1, 4) and B(6, -1). If point C divides in the ratio 2 : 3, the coordinates of C are . If point D divides
    7·2 answers
  • What is the factorization of the polynomial below<br>-x^2 - 15x - 56​
    6·1 answer
  • H(x) = -x3 + 2x2 + 8x<br><br> what are the zeros and the terminal behaviour
    10·1 answer
  • Find the volume of the box
    11·1 answer
  • If m ABC = 125°, and mZABD = 949,<br> then m2DBC = [? ]°
    6·1 answer
  • If a is directly proportional to b, and a = 25 when b = 35, find b when a = 40
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!