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Let C1 and C2 be two biased coins such that the probabilities of getting head in a single toss are 2/3 and 1/3, respectively. Suppose α is the number of heads that appear when C1 is tossed twice, independently, and suppose b is the number of heads that appear when C2 is tossed twice, independently, Then probability that the roots of the quadratic polynomial x2 – αx + β are real and equal, is
  • a)
    40/81
  • b)
    20/81
  • c)
    1/2
  • d)
    1/4
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Let C1 and C2 be two biased coins such that the probabilities of getti...

For C1

For C2

for real and equal roots 
α2 = 4β
(α, β) = (0, 0), (2, 1)
So, probability = 
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Most Upvoted Answer
Let C1 and C2 be two biased coins such that the probabilities of getti...
We randomly pick one of the coins and toss it twice. Let A be the event that we get two heads, and let B be the event that we get at least one head.

To find P(A), we can use the law of total probability. Let C be the event that we picked coin C1, and let D be the event that we picked coin C2. We want to find P(A), so we can consider two cases:

Case 1: We picked coin C1
P(A|C1) = (2/3)^2 = 4/9
P(C1) = 1/2

Case 2: We picked coin C2
P(A|C2) = (1/3)^2 = 1/9
P(C2) = 1/2

Using the law of total probability, we have:
P(A) = P(A|C1)P(C1) + P(A|C2)P(C2)
= (4/9)(1/2) + (1/9)(1/2)
= 2/9 + 1/18
= 5/18

To find P(B), we can use the complement rule. The complement of event B (not getting at least one head) is getting two tails. Since we have two possible outcomes (coin C1 or C2), we can consider two cases:

Case 1: We picked coin C1
P(two tails|C1) = (1/3)^2 = 1/9
P(C1) = 1/2

Case 2: We picked coin C2
P(two tails|C2) = (2/3)^2 = 4/9
P(C2) = 1/2

Using the law of total probability, we have:
P(B) = 1 - P(two tails)
= 1 - (P(two tails|C1)P(C1) + P(two tails|C2)P(C2))
= 1 - (1/9)(1/2) - (4/9)(1/2)
= 1 - 1/18 - 2/9
= 1 - 1/18 - 4/18
= 1 - 5/18
= 13/18

Therefore, the probability of getting two heads is 5/18, and the probability of getting at least one head is 13/18.
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Let C1 and C2 be two biased coins such that the probabilities of getting head in a single toss are 2/3and 1/3, respectively. Supposeα is the number of heads that appear when C1 is tossed twice,independently, and suppose b is the number of heads that appear when C2 is tossed twice, independently, Then probability that the roots of the quadratic polynomial x2 – αx + β are real and equal, isa)40/81b)20/81c)1/2d)1/4Correct answer is option 'B'. Can you explain this answer?
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Let C1 and C2 be two biased coins such that the probabilities of getting head in a single toss are 2/3and 1/3, respectively. Supposeα is the number of heads that appear when C1 is tossed twice,independently, and suppose b is the number of heads that appear when C2 is tossed twice, independently, Then probability that the roots of the quadratic polynomial x2 – αx + β are real and equal, isa)40/81b)20/81c)1/2d)1/4Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let C1 and C2 be two biased coins such that the probabilities of getting head in a single toss are 2/3and 1/3, respectively. Supposeα is the number of heads that appear when C1 is tossed twice,independently, and suppose b is the number of heads that appear when C2 is tossed twice, independently, Then probability that the roots of the quadratic polynomial x2 – αx + β are real and equal, isa)40/81b)20/81c)1/2d)1/4Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let C1 and C2 be two biased coins such that the probabilities of getting head in a single toss are 2/3and 1/3, respectively. Supposeα is the number of heads that appear when C1 is tossed twice,independently, and suppose b is the number of heads that appear when C2 is tossed twice, independently, Then probability that the roots of the quadratic polynomial x2 – αx + β are real and equal, isa)40/81b)20/81c)1/2d)1/4Correct answer is option 'B'. Can you explain this answer?.
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