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Probability Ncert Solutions Maths class 12th Maths Class 12th Probability

Choose the correct answer in each of the following:

Q.65. The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is:

(A) 1

(B) 2

(C) 5

(D) $\frac{8}{3}$

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

4 months ago

65. Let X be the random variable representing a number on the die.

The total number of observations is six.

$\begin{array}{l} ∴ P (X = 1) = \frac{3}{6} = \frac{1}{2} \\ P (X = 2) = \frac{2}{6} = \frac{1}{3} \\ P (X = 5) = \frac{1}{6} \end{array}$

Therefore, the probability distribution is as follows.

X	1	2	5
P (X)	1/2	1/3	1/6

$M e a n = E (X) = \sum_{}^{} P_{i} X_{i}$

$\begin{array}{l} = \frac{1}{2} \times 1 + \frac{1}{3} \times 2 + \frac{1}{6} \times 5 \\ = \frac{1}{2} + \frac{2}{3} + \frac{5}{6} \\ = \frac{3 + 4 + 5}{6} \\ = \frac{12}{6} \\ = 2 \end{array}$

Therefore, option (B) is correct.

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Let a die rolled till 2 is obtained. The probability that 2 obtained on even numbered toss is equal to

alok kumar singh

P (2 obtained on even numbered toss) = k (let)

P (2) = $\frac{1}{6}$

P ( $\bar{2}$ )= $\frac{5}{6}$

$k = \frac{5}{6} \times \frac{1}{6} + {(\frac{5}{6})}^{3} \times \frac{1}{6} + {(\frac{5}{6})}^{5} \times \frac{1}{6} + . . .$

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Given set S = {0, 1, 2, 3, ….., 10}. If a random ordered pair (x, y) of elements of S is chosen, then find probability that |x – y| > 5

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If x = 0, y = 6, 7, 8, 9, 10

If x = 1, y = 7, 8, 9, 10

If x = 2, y = 8, 9, 10

If x = 3, y = 9, 10

If x = 4, y = 10

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A bag contains 8 balls (black and white). If four balls are chosen without replacement then 2W and 2B are found then the probability that number of white and black balls are same in bag is equal to

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+ P (3B, 5W) × P (2W and 2B)

+ P (4B, 4W) × P (2W and 2B)

+ P (5B, 3W) × P (2W and 2B)

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Let probability of tail is $\frac{1}{3}$

⇒ Probability of getting head = $\frac{2}{3}$

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The coefficients a, b and c of the quadratic equation, ax² + bx + c = 0 are obtained by throwing a dice three times. The probability that this equation has equal roots is:

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ax² + bx + c = 0

D = b² – 4ac

D = 0

b² – 4ac = 0

b² = 4ac

(i) AC = 1, b = 2 (1, 2, 1) is one way

(ii) AC = 4, b = 4

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(iii) AC = 9, b = 6, a = 3, c = 3 is one way

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Choose the correct answer in each of the following:

Q.65. The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is:

(A) 1

(B) 2

(C) 5

(D) $\frac{8}{3}$

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Choose the correct answer in each of the following: Q.65. The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is: (A) 1 (B) 2 (C) 5 (D) 83

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Choose the correct answer in each of the following:

Q.65. The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is:

(A) 1

(B) 2

(C) 5

(D) $\frac{8}{3}$