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

Probability

Q.3. A class consists of 50 students out of which there are 10 girls. In the class 2 girls and 5 boys are rank holders in an examination. If a student is selected at random from the class and is found to be a rank holder, what is the probability that the student selected is a girl ?

Solution :

Probability of girl rank holder = P(G/R)
= [P(R/G).P(G)]/[P(R/G).P(G)+P(R/B).P(B)]
= [(1/5)×(1/5)]/[(1/5)×(1/5)+(4/5)×(5/40)]
= [1/25]/[(1/25)+(1/10)]
= [1/25]/[(2+5)/50]
=[1/25]/[7/50]
= (1/25)×(50/7) = 2/7 . [Ans.]

Q.4. A man is known to speak the truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually a six.

Solution :

Let E1 be the event of occurring of six and E2 the event of not occurring of six.
Therefore, P(E₁) = P(Getting a six) = 1/6
And P(E₂) = P(Not getting a six) = 1 – 1/6 = 5/6.
Let E be the event that a man throws a die and he reports that it is a six.
Therefore, P(E/E₁) = 3/4 and P(E/E2) = 1 – 3/4 = 1/4.
By Baye’s Theorem,
P(Six) = P(E₁/E) = [P(E₁)P(E/E₁)]/[P(E₁)P(E/E₁) + P(E₂)P(E/E₂)]
= [(1/6×3/4)]/[(1/6×3/4) + (5/6×1/4)]
= (3/24)/[(3/24) + (5/24)]
= (3/24)×(24/8)
= 3/8. [Ans.]

Q.5. An insurance company insured 1500 scooter drivers, 2500 car drivers and 4500 truck drivers. The probability of a scooter, a car and a truck meeting with an accident is 0.01, 0.02 and 0.04 respectively. If one of the insured persons meets with an accident, find the probability that he is a scooter driver.

Solution :

Probability of accident by scooter
= P(Accident/Scooter) = P(A/S)
= [P(S).P(S/A)]/[P(S).P(S/A) + P(C).P(C/A) + P(T).P(T/A)]
= [(1500/8500)×0.01]/[(1500/8500)×0.01 + (2500/8500)×0.02 + (4500/8500)×0.04]
= 15/245 = 3/49 . [Ans.]

Q.6. A company has two plants which manufacture scooters. Plant I manufactures 80% of the scooters while Plant II manufactures 20% of the scooters. At Plant I, 85 out of 100 scooters are rated as being of standard quality, while at Plant II only 65 out of 100 scooters are rated as being of standard quality. If a scooter is of standard quality , what is the probability that it come from Plant I.

Solution :

Let A and B denotes the scooters manufactured in Plant I and Plant II respectively , then
Probability P(A) = 80/100 = 0.8 & P(B) = 20/100 = 0.2
Let X represent the event that scooter manufactured is of standard quality , then P(X/A) = 85/100 = 0.85 & P(X/B) = 65/100 = 0.65 .
Applying Baye’s Theorem , the probability of selected scooter is of standard quality produced by Plant I ,
P(A/X) = [P(A) P(X/A)]/[P(A)P(X/A) + P(B)P(X/B)]
= [0.8×0.85]/[(0.8 ×0.85) + (0.2×0.65)]
= 0.68/(0.68 + 0.13) = 0.68/0.81 = 68/81 = 0.84 .[Ans.]

Paper By Mr. M.P.Keshari
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