India plays two matches each with West Indies and Australia. In any ma

Question

India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points 0, 1 and 2 are 0.45, 0.05 and 0.5 respectively. Assuming that the outcomes are independent, the probability of India getting at least 7 points is

A. 0.0625
B. 0.06875
C. 0.0825
D. 0.0875
E. 0.875

A. 0.0625
B. 0.06875
C. 0.0825
D. 0.0875
E. 0.875

Lampard42 · Answer

Atleast 7 points means 7 and 8 points (4 wins or 3 wins and 1 draw). So 4 wins prob=(.5)^4=.0625 and 3Wins and 1 draw = (0.5)^3*.05*4ways of it happening=.025 Adding both .0875 IMO D

CareerGeek · Answer

Assume 0 points = Loss (L), 1 point = Draw (D), 2 points = Win (W)
So, Prob(L) = 0.45, Prob(D) = 0.05, Prob(W) = 0.5

To get at least 7 points --> 7 points (3W&1D) or 8 points (4W)

Required Probability = 4c1* (0.5)^3 (0.05) +  (0.5)^4 
= 4*0.00625 + 0.0625
= 0.0250 + 0.0625
= 0.0875

IMO Option D

Pls Hit Kudos if you like the solution

EgmatQuantExpert · Answer

Solution

Given: 
 • India plays two matches each with West Indies and Australia 
• The probabilities of India getting points 0, 1 and 2 are 0.45, 0.05 and 0.5

To Find: 
 • The probability of India getting at least 7 points

Approach & Working Out: 
 • The probability of India getting at least 7 points = The probability of India getting four 2’s + the probability of India getting three 2’s + one 1 =  (0.5)^4 + ^4C_1 * 0.5 * 0.5 * 0.5 * 0.05 = 0.0875

Hence, the correct answer is  Option D

ScottTargetTestPrep · Answer

In order to get at least 7 points in 4 matches, you must get 4 matches of 2 points each OR 3 matches of 2 points each and 1 match of 1 point.

The probability of getting 4 matches of 2 points each is:

0.5 x 0.5 x 0.5 x 0.5 = 0.5^4 = 0.0625

The probability of getting 3 matches of 2 points each and 1 match of 1 point is (notice that 4!/3! Is the number of ways to arrange the 3 matches of 2 points and 1 match of 1 point):

(0.5 x 0.5 x 0.5 x 0.05) x 4!/3! = 0.00625 x 4 = 0.025

Therefore, the probability of getting at least 7 points is:

0.0625 + 0.025 = 0.0875

Answer: D

punyaslok · Answer

Given: 
The probabilities of India getting points 0, 1 and 2 are 0.45, 0.05 and 0.5 respectively
Outcomes are independent

To find: 
The probability of India getting at least 7 points

Process:
To get 7 or 8 points, India has to win 3 matches & draw 1 match (7 points) or win 4 matches (8 points)

Probability of 4 wins = (0.5)^4 = 0.0625 
Probability of 3 wins and 1 draw = (0.5)^3 * (0.05) * 4 = 0.025 
Adding both the probabilities, we get: 0.0875

Hence, the correct option is D

merajul · Answer

India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points 0, 1 and 2 are 0.45, 0.05 and 0.5 respectively. Assuming that the outcomes are independent, the probability of India getting at least 7 points is

A. 0.0625
B. 0.06875
C. 0.0825
D. 0.0875
E. 0.875

A. 0.0625
B. 0.06875
C. 0.0825
D. 0.0875
E. 0.875

AND or BOTH = you have to multiply the events
OR = you have to add the events
 
Total events = 4, since India play 2 matches each with WI & Australia.
At least 7 Points ,i.e = score >=7

So following options should be considered -

a)2+2+2+2 = 8  (0.5)^4 ] 
b)2+2+2+1 = 7  
c)2+2+1+2 = 7  
d)2+1+2+2 = 7  
e)1+2+2+2 = 7  .....or (b-e) =  4C1 X (0.5)^3 X 0.05

Now as a whole, the probability shall be   =  0.0875 (Answer D)

Wadree · Answer

Only ways to get at least 7 are.... 2 + 2 + 2 + 2 = 8 ... And 2 + 2 + 2 + 1 = 7.....
So.... 4 times 2 can happen in only 1 way......
Now.....in second scenario..... India will get 2 point any 3 times among da 4 matches.... And will get 1 point any 1 time among da 4 matches...... So how many ways can that happen?
Lets think like this .... India will get 1 point in .... first match ... Or second match...or third match...or fourth match....
So 4 possible sub scenario of 2 + 2 + 2 + 1 = 7 scenario......

Now probability of 2 + 2 + 2 + 2 = 8 .......is...... 0.5 × 0.5 × 0.5 × 0.5 = 0.0625

And probability of 2 + 2 + 2 + 1 = 7 .....is...... 0.5 × 0.5 × 0.5 × 0.05 = 0.00625
But ... 2 + 2 + 2 + 1 = 7 can happen in 4 ways....so probability of 2 + 2 + 2 + 1 = 7 .....is...... 0.00625 × 4 = 0.025

So total probability of India getting at least 7 points is = 0.0625 + 0.025 = 0.0875 .......

!nah id win!

India plays two matches each with West Indies and Australia. In any ma

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India plays two matches each with West Indies and Australia. In any ma

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