CBSE Guess > Papers > Important Questions > Class XII > 2010 > Maths > Mathematics By Mr. M.P.Keshari

Probability

Q.2. If the mean and variance of the binomial distribution are respectively 9 and 6, find the distribution.

Solution :

We have, mean = np = 9 and variance = npq = 6
Therefore, npq/np = 6/9 => q = 2/3 and p = 1 – q = 1 – 2/3 = 1/3.
From np = 9 => n = 9/p = 27.
Therefore, Binomial Distribution is (q + p)n = (2/3 + 1/3)²⁷.[Ans.]

Q.3. In a box containing 50 bulbs, 5 are defective. What is the probability that a sample of 5 bulbs will have at most 2 defective bulbs?

Solution :

We have, p = P(defective bulb) = 5/50 = 0.1 and q = 1 – p = 1 – 0.1 = 0.9.
Binomial distribution is given by (q + p)ⁿ; where n = 5.
Therefore, P(X = r) = ⁵C_rq^{5 – r} p^r = 5Cr(0.9)5 – r (0.1)r.
Now, P( X≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
= ⁵C₀(0.9)⁵ + ⁵C₁(0.9)⁴(0.1) + ⁵C₂(0.9)³(0.1)²
= (0.9)³[0.81 + 5 ×0.9×0.1 + 10×0.01]
= 0.729[0.81 + 0.45 + 0.1]
= 0.729 × 1.36 = 0.99.[Ans.]

Q.4. The probability of hitting a target by A is 1/5. If he fires 5 times, find the probability that he will hit at least two times.

Solution :

We have, p = 1/5, q = 4/5 and n = 5.
Therefore, P(X = x) = ⁵C_x(4/5)^5–x(1/5)^x.
≥2) = 1 – P(X = 0) – P(X = 1) = 1 – ⁵C₀(4/5)⁵(1/5)⁰ – ⁵C₁(4/5)4(1/5)1 = 1 – 1024/3125 – 821/3125 = 821/3125.[Ans.]

Paper By Mr. M.P.Keshari
Email Id : [email protected]
Ph No. : 09434150289