# Recent questions tagged probability

1
There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag. The probability that at least two chocolates are identical is _________ $0.3024$ $0.4235$ $0.6976$ $0.8125$
2
A normal random variable has mean equal to $0$, and standard deviation equal to $3$. The probability that on a random draw the value of this random variable is greater than $0$ is __________ (round off to $2$ decimal places).
3
For the probability density $P(x) = 0.5e^{-0.5x}$, the integral $\displaystyle \int_0^{\infty}P(x)dx =$ __________
4
In any given year, the probability of an earthquake greater than Magnitude $6$ occurring in the Garhwal Himalayas is $0.04$. The average time between successive occurrences of such earthquakes is_____ years.
5
$10\%$ of the population in a town is HIV+. A new diagnostic kit for HIV detection is available; this kit correctly identifies HIV+ individuals 95% of the time, and HIV individuals $89\%$ of the time. A particular patient is tested using this kit and is found to be positive. The probability that the individual is actually positive is_______
6
If an unbiased coin is tossed $10$ times, the probability that all outcomes are same will be_______ $\times 10^{-5}$
7
In a factory, two machines $M1$ and $M2$ manufacture $60\%$ and $40\%$ of the autocomponents respectively. Out of the total production $2\%$ of $M1$ and $3\%$ of $M2$ are found to be defective. If a randomly drawn autocomponent from the combined lot is found defective, what is the probability that it was manufactured by $M2$? $0.35$ $0.45$ $0.5$ $0.4$
8
An automobile plant contracted to buy shock absorbers from two suppliers $X$ and $Y$. $X$ supplies $60\%$ and $Y$ supplies $40 \%$ of the shock absorbers. All shock absorbers are subjected to a quality test. The ones that pass the quality test are considered reliable. Of $X's$ ... a randomly chosen shock absorber, which is found to be reliable, is made by $Y$ is $0.288$ $0.334$ $0.667$ $0.720$
9
A disease is inherited by a child with a probability of $1/4$. In a family with two children, the probability that exactly one sibling is affected by this disease is $1/4$ $3/8$ $7/16$ $9/16$
The probability distribution for a discrete random variable $X$ is given below. $\begin{array}{|c|c|c|c|c|} \hline X & 1 & 2 & 3 & 4 \\ \hline P(X) & 0.3 & 0.4 & 0.2 & 0.1 \\ \hline \end{array}$The expectation value of $X$ is (up to one decimal place) _____________
The variable $z$ has a standard normal distribution. If $P(0 \leq z \leq 1)= 0.34$ then $P(z^2 > 1)$ is equal to (up to two decimal places) ____________
Consider an unfair coin. The probability of getting heads is $0.6$. If you toss this coin twice, what is the probability that the fast or the second toss is heads? $0.56$ $0.64$ $0.84$ $0.96$