A biased die is such that probability of getting 2 is $\frac{1}{10}$ and other scores being equally likely. The die is tossed twice and X denotes number of 2 obtained. Which of the following are correct ?
(A) The possible values of X are 0, 1, 2, 3, 4.
(B) The possible values of X are 0, 1, 2.
(C) Probability of getting at least one 2 is 0.046.
(D) Probability of getting at least one 2 is 0.19.
(E) Mathematical expectation of X : E(X) = 0.18.
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (B) and (D) Only
(B) X represents the number of times a 2 appears in two tosses of the die.
$X=0$ (no 2's appear)
$X=1$ (one 2 appears)
$X=2$ (both are 2's)
X ∼ Binomial $(n=2,p=\frac{1}{10})$
(D) $E(X)=np=2×\frac{1}{10}=0.2≃0.18$