A random variable X has the following probability distribution:, X, 0, 1, 2, 3, 4, 5, 6, P(X), z, 2z, 2z, 3z, z^2, 2z^2, 7z^2+z, Which of the following are TRUE? (A) P(X 4) = 0.2 (C) The value of z is 0.1 (D) P(3≤ X<5) = 0.31 Choose the correct answer from the options given below: Option 1: (A) and (C) only Option 2: (B) and (D) only Option 3: (A) and (B) only Option 4: (C) and (D) only

Answer: (C) and (D) only. Solution: Sum of probabilities: 10z^2+9z=1(10z-1)(z+1)=0 z=0.1, so (C) is true. P(X 4)=2z^2+7z^2+z=9z^2+z=0.19, so (B) fails. P(3≤ X<5)=3z+z^2=0.30+0.01=0.31, so (D) is true.

Algebra

Probability

Hard

applied

A random variable X has the following probability distribution:

X 0 1 2 3 4 5 6
P(X) z 2z 2z 3z $z^2$ $2z^2$ $7z^2+z$

Which of the following are TRUE?

(A) P(X < 3) = 0.8

(B) P(X > 4) = 0.2

(C) The value of z is 0.1

(D) $P(3\le X<5) = 0.31$

Choose the correct answer from the options given below:

X	0	1	2	3	4	5	6
P(X)	z	2z	2z	3z	$z^2$	$2z^2$	$7z^2+z$

(A) and (C) only

(B) and (D) only

(A) and (B) only

✅ Correct Option: 4

Sum of probabilities: $10z^2+9z=1\Rightarrow(10z-1)(z+1)=0\Rightarrow z=0.1$ , so (C) is true.

$P(X<3)=5z=0.5$ , so (A) fails.

$P(X>4)=2z^2+7z^2+z=9z^2+z=0.19$ , so (B) fails.

$P(3\le X<5)=3z+z^2=0.30+0.01=0.31$ , so (D) is true.

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Mean and variance of a binomial distribution are 6 and 2 respectively. The probability of 2 successes will be

2025: 3 June Shift 1

If A and B are independent events, then which of the following is not true?

2025: 15 May Shift 2

A die is tossed 6 times and getting "1 or 5" is considered a success. The probability of getting at least one success in six tosses is:

2022: 7 Aug Shift 2

A shopkeeper sells three types of flower seeds $A_1, A_2, A_3$ . They are sold as a mixture where the proportions are 4 : 4 : 2 respectively. The germination rates of the three types of seeds are 45%, 60% and 35% respectively. Calculate the probability in the following cases.

The probability of a randomly chosen seed to germinate is :

2025: 13 May Shift 2

Which of the following statements are NOT correct about Standard Normal Distribution?

(A) The probability curve of the Standard Normal Distribution is a bell-shaped curve.

(B) The Standard Normal variate (Z) score describes the position of each data point in terms of its distance from the mean, when measured in standard deviation units.

(D) There is a 95.45 % probability of randomly selecting a score between $\mu - \sigma$ and $\mu + \sigma$ , when $\sigma$ is standard deviation and $\mu$ is mean.

Choose the correct answer from the options given below:

2025: 15 May Shift 2

A player participates in 3 matches against three teams T₁, T₂ and T₃.The probability of winning a match against teams T₁, T₂ and T₃ are 0.2, 0.3 and 0.9 respectively. If 'wins' can be regarded as independent events, then the probability that he

(A) wins all the 3 matches is 0.054

(B) wins no match is 0.054

(D) wins exactly one match is 0.542

Choose the correct answer from the options given below:

Solution

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