List of top Logical Reasoning Questions on Probability asked in GATE EY

In a forest, there are tigers, hare, and deer. On a given day, the probability of a tiger hunting a hare is 0.35, a deer is 0.25, and either a hare or a deer is 0.55. The probability of a tiger hunting both a hare and a deer on a given day is \_\_\_\_\_\_\_\_, (Round off to two decimal places).

Consider a discrete random variable \( X \) that takes values from the set \( S = \{0, 1, 2, 3\} \), being the number of individuals of a species within a habitat. Consider the probability distribution of \( X \) with \( Pr(X = 0) = 0.15 \), \( Pr(X = 1) = 0.25 \), and \( Pr(X = 3) = 0.5 \), where \( Pr \) denotes probability. The value of \( Pr(X = 2) \) is \_\_\_\_\_\_\_\_. (Round off to two decimal places).

There are two species, X and Y, with abundances \(x\) and \(y\), respectively. Species X has growth rate \(\alpha\), and species Y has growth rate \(\beta\). Assume that the sum of the species abundances is constant over time, i.e., \(x + y = 1\). Let \(x\) and \(y\) follow the rate equations: \[ \frac{dx}{dt} = \alpha x - \varphi x, \quad \frac{dy}{dt} = \beta y - \varphi y, \] where \(\varphi\) is the average species fitness. Which one of the following options correctly represents the expression for \(\varphi\)?

The abundance (X) of a plant species with respect to the anthropogenic stressor habitat destruction (h) is shown. The solid and the dashed curves represent stable and unstable population equilibrium abundances, respectively. \includegraphics[width=0.5\linewidth]{45a.png}
In the absence of any stochasticity, and with increasing values of h, what is the value of h at which a sudden population collapse would occur?

An ecologist must determine whether (i) the means of two independent samples differ, and (ii) there is an association between two continuous variables. Assuming that all samples are normally distributed, which one of the following options represents the most appropriate statistical tests for (i) and (ii), respectively?

Male voles pair with either a single female (monogamous) or with two females (polygynous) during a given breeding season. The probability of a male being polygynous in a breeding season is 0.2. The reproductive success (number of offspring) of monogamous males is 2, and of polygynous males is 3. A male’s expected reproductive success in a breeding season is \_\_\_\_\_\_\_\_\_\_\_. (Round off to one decimal place)